Imaging apparatus having a curved image surface

ABSTRACT

Provided is an imaging apparatus, including: an imaging optical system including a plurality of lenses; and an image plane which is disposed on an image side of the imaging optical system and is curved so that a concave surface thereof faces an object side of the imaging optical system. The imaging optical system includes an aperture stop. In the imaging optical system, a lens closer to the object side than the aperture stop and a lens closer to the image side than the aperture stop have different positive powers. A focal length of the imaging optical system is substantially equal to a distance from an exit pupil of the imaging optical system to the image plane. A radius of curvature of the image plane is substantially equal to the focal length of the imaging optical system.

This application is a division of application Ser. No. 13/792,841 filedMar. 11, 2013.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an imaging apparatus in which a curvedimage plane (i.e., curved image surface) is disposed near an image planeof an imaging optical system. In particular, the present inventionprovides an imaging apparatus suitable for a digital still camera, adigital video camera, a cell phone camera, a monitoring camera, and thelike.

2. Description of the Related Art

There are disclosed some examples of the imaging apparatus using such acurved image plane. There is proposed a ball lens in which a sphericalshell lens and a spherical lens disposed inside the lens constituteconcentric spheres (Japanese Patent Application Laid-Open No.S63-081413).

This ball lens can appropriately correct spherical aberration andchromatic aberration.

In addition, because of the point symmetry structure of the ball lens,it is easy to realize a wider angle of field, and hence the ball lens issuitable for an imaging optical system of an imaging apparatus requiredto have a wide angle and high resolution.

There is disclosed an example of the ball lens in which an aperture stopis disposed on a plane passing through the spherical center of the balllens in order to obtain good imaging performance by blocking harmfullight such as flare.

In addition, there is proposed an imaging optical system in which animage sensor surface is curved in a two-dimensional manner (JapanesePatent No. 4628781).

Japanese Patent No. 4628781 discloses an example in which, in order toreduce constraint in a case where an image sensor serves as an imagerecording medium, a light receiving plane of the image sensor is madeconcave to the object side so that an incident angle of a light beam tothe image sensor becomes closer to the normal angle.

There is disclosed an optical system formed of only two single-lensmembers and an aperture stop therebetween, in which one of the lensmembers has aspherical surfaces on both sides for the purpose of use inan inexpensive camera having a curved image plane (Japanese PatentApplication Laid-Open No. H08-338944). This optical system has a fullangle of field of at least 62.5 degrees and is an imaging apparatus fora disposable camera in which an image is formed on a curved film plane.

In an imaging apparatus in recent years, a pixel size of the imagesensor has been rapidly reduced, and the imaging optical system isrequired to have a higher resolution. Therefore, the imaging opticalsystem is required to realize high imaging performance even at a small Fvalue.

Further, in recent years, the imaging apparatus are required to have awider angle and a smaller size.

Japanese Patent Application Laid-Open No. S63-081413 discloses anexample of using a ball lens, and, in a main example, an imaging opticalsystem has F/2.8 and has good imaging performance in which sphericalaberration and axial chromatic aberration are appropriately corrected.

On the other hand, there is also disclosed an example in which an Fvalue is smaller than F/2.8. For instance, there is disclosed an imagingoptical system having F/2.0 or F/1.4. However, in such a small F value,large spherical aberration is generated, and sufficient imagingperformance cannot be obtained.

In other words, in the imaging optical system having an F value smallerthan F/2.0, in particular, spherical aberration cannot be correctedsufficiently only by the ball lens, and hence there is a problem in thatthe imaging performance is deteriorated. In addition, there is alsodisclosed an imaging optical system having F/1.0, in which aberration iscorrected by using a high refractive index material such as N=2.500 orN=2.301.

Such a high refractive index material is expensive, and there may causea problem in that transmittance thereof is deteriorated.

Japanese Patent No. 4628781 discloses an example using a point asymmetryimaging optical system, in which aberrations such as sphericalaberration, axial chromatic aberration, and field curvature arecorrected in a relatively small F value of F/2.45 to F/2.91 of theimaging optical system, and hence high imaging performance is realized.However, in the imaging apparatus in recent years, a pixel size of theimage sensor is reduced to be very small, and an optical system having ahigher resolution is demanded. Therefore, in the imaging optical systemhaving an F value smaller than F/2.0, it is a problem in that aberrationsuch as spherical aberration occurs, resulting in deterioration of theimaging performance.

In the optical system of Japanese Patent Application Laid-Open No.H08-338944, the image plane is curved, and the two single-lens membershave aspherical surfaces. Thus, the imaging performance is improved overthe wide angle. However, this optical system reduces generation amountof spherical aberration by narrowing focus to F/8.0. In addition, inthis optical system, the surface closest to the object side is providedwith an aspherical surface that is displaced from the referencespherical surface toward the image side, and the surface closest to theimage side is provided with an aspherical surface that is displaced fromthe reference spherical surface toward the object side. In other words,these aspherical surfaces are displaced from the reference sphericalsurfaces to the inside of the imaging optical system in peripheries ofthe lens surfaces disposed on the outermost sides of the imaging opticalsystem. The aspherical surfaces correct coma and astigmatism. Therefore,spherical aberration cannot be corrected appropriately.

SUMMARY OF THE INVENTION

The present invention provides an imaging apparatus that can obtain highimaging performance by appropriately correcting aberration at a small Fvalue.

According to one exemplary embodiment of the present invention, there isprovided an imaging apparatus, including: an imaging optical systemincluding a plurality of lenses; and an image plane which is disposed onan image side of the imaging optical system and is curved so that aconcave surface thereof faces an object side of the imaging opticalsystem, in which: the imaging optical system includes an aperture stop;a lens disposed in the object side of the aperture stop in the imagingoptical system and a lens disposed in the image side of the aperturestop in the imaging optical system have different positive powers; afocal length of the imaging optical system is substantially equal to adistance from an exit pupil of the imaging optical system to the imageplane; and a radius of curvature of the image plane is substantiallyequal to the focal length of the imaging optical system.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating a structural example of an imagingapparatus according to Example 1 of the present invention.

FIG. 2 is an axial aberration diagram of an imaging optical systemaccording to Example 1 of the present invention.

FIG. 3 is a lateral aberration diagram of the imaging optical systemaccording to Example 1 of the present invention.

FIG. 4 is a diagram illustrating a structural example of an imagingapparatus according to Example 2 of the present invention.

FIG. 5 is an axial aberration diagram of an imaging optical systemaccording to Example 2 of the present invention.

FIG. 6 is a lateral aberration diagram of the imaging optical systemaccording to Example 2 of the present invention.

FIG. 7 is a diagram illustrating a structural example of an imagingapparatus according to Example 3 of the present invention.

FIG. 8 is an axial aberration diagram of an imaging optical systemaccording to Example 3 of the present invention.

FIG. 9 is a lateral aberration diagram of the imaging optical systemaccording to Example 3 of the present invention.

FIG. 10 is a diagram illustrating a structural example of an imagingapparatus according to Example 4 of the present invention.

FIG. 11 is an axial aberration diagram of an imaging optical systemaccording to Example 4 of the present invention.

FIG. 12 is a lateral aberration diagram of the imaging optical systemaccording to Example 4 of the present invention.

FIG. 13A is a diagram illustrating an imaging relationship when anobject plane of the imaging apparatus according to an embodiment of thepresent invention is disposed at a finite distance.

FIG. 13B is a diagram illustrating an imaging relationship when theobject plane of the imaging apparatus according to the embodiment of thepresent invention is disposed at a finite distance.

FIG. 14 is a diagram showing a relationship between an in-focus positionand a shape of an image plane when focus adjustment is performed in theimaging apparatus according to the embodiment of the present invention.

FIG. 15 is a diagram illustrating a structural example of an imagingapparatus according to Example 5 of the present invention.

FIG. 16 is a schematic diagram of a wave front control unit of theimaging apparatus according to Example 5 of the present invention.

FIG. 17 is a schematic diagram of the wave front control unit of theimaging apparatus according to Example 5 of the present invention.

FIG. 18 is a schematic diagram of the wave front control unit of theimaging apparatus according to Example 5 of the present invention.

FIG. 19 is a schematic diagram of the wave front control unit of theimaging apparatus according to Example 5 of the present invention.

FIG. 20 is a schematic diagram of the wave front control unit of theimaging apparatus according to Example 5 of the present invention.

FIG. 21 is a diagram showing a phase difference distribution given to awave front control element of the imaging apparatus according to Example5 of the present invention.

FIG. 22 is a diagram showing a power difference due to a phasedifference of the wave front control element of the imaging apparatusaccording to Example 5 of the present invention.

FIG. 23 is an axial aberration diagram of an imaging optical systemaccording to Example 5 of the present invention.

FIG. 24 is a lateral aberration diagram of the imaging optical systemaccording to Example 5 of the present invention.

FIG. 25 is a diagram illustrating a structural example of an imagingapparatus according to Example 6 of the present invention.

FIG. 26 is a diagram showing a phase difference distribution given to awave front control element according to Example 6 of the presentinvention.

FIG. 27 is a diagram showing a power difference due to a phasedifference of the wave front control element according to Example 6 ofthe present invention.

FIG. 28 is an axial aberration diagram of an imaging optical systemaccording to Example 6 of the present invention.

FIG. 29 is a lateral aberration diagram of the imaging optical systemaccording to Example 6 of the present invention.

FIG. 30 is a diagram illustrating a structural example of an imagingapparatus according to Example 7 of the present invention.

FIG. 31 is a diagram showing a power difference due to a phasedifference of a wave front control element according to Example 7 of thepresent invention.

FIG. 32 is an axial aberration diagram of an imaging optical systemaccording to Example 7 of the present invention.

FIG. 33 is a lateral aberration diagram of the imaging optical systemaccording to Example 7 of the present invention.

FIG. 34 is a diagram illustrating a structural example of an imagingapparatus according to Example 8 of the present invention.

FIG. 35 is an axial aberration diagram of the imaging optical systemaccording to Example 8 of the present invention.

FIG. 36 is a lateral aberration diagram of the imaging optical systemaccording to Example 8 of the present invention.

FIG. 37 is a diagram illustrating a structural example of an imagingapparatus according to Example 9 of the present invention.

FIG. 38 is an axial aberration diagram of an imaging optical systemaccording to Example 9 of the present invention.

FIG. 39 is a lateral aberration diagram of the imaging optical systemaccording to Example 9 of the present invention.

FIG. 40 is a diagram illustrating a structural example of an imagingapparatus according to Example 10 of the present invention.

FIG. 41A is a diagram showing an aspherical amount of an imaging opticalsystem used for the imaging apparatus according to Example 10 of thepresent invention.

FIG. 41B is a diagram showing the aspherical amount of the imagingoptical system used for the imaging apparatus according to Example 10 ofthe present invention.

FIG. 42A is a diagram illustrating the aspherical amount of the imagingoptical system used for the imaging apparatus according to Example 10 ofthe present invention.

FIG. 42B is a diagram illustrating the aspherical amount of the imagingoptical system used for the imaging apparatus according to Example 10 ofthe present invention.

FIG. 43 is an axial aberration diagram of the imaging optical systemaccording to Example 10 of the present invention.

FIG. 44 is a lateral aberration diagram of the imaging optical systemaccording to Example 10 of the present invention.

FIG. 45 is a diagram illustrating a structural example of an imagingapparatus according to Example 11 of the present invention.

FIG. 46A is a diagram showing an aspherical amount of an imaging opticalsystem used for the imaging apparatus according to Example 11 of thepresent invention.

FIG. 46B is a diagram showing the aspherical amount of the imagingoptical system used for the imaging apparatus according to Example 11 ofthe present invention.

FIG. 47 is a diagram showing the aspherical amount of the imagingoptical system used for the imaging apparatus according to Example 11 ofthe present invention.

FIG. 48 is an axial aberration diagram of the imaging optical systemaccording to Example 11 of the present invention.

FIG. 49 is a lateral aberration diagram of the imaging optical systemaccording to Example 11 of the present invention.

FIG. 50 is a diagram illustrating a structural example of an imagingapparatus according to Example 12 of the present invention.

FIG. 51A is a diagram showing an aspherical shape of a lens surfaceclosest to the object side in the imaging apparatus according to Example12 of the present invention.

FIG. 51B is a diagram showing an aspherical amount of the lens surfaceclosest to the object side in the imaging apparatus according to Example12 of the present invention.

FIG. 52A is a diagram showing a second order differential value of anaspherical surface and a reference spherical surface of the lens surfaceclosest to the object side in the imaging apparatus according to Example12 of the present invention.

FIG. 52B is a diagram showing a second order differential value of anaspherical component of the lens surface closest to the object side inthe imaging apparatus according to Example 12 of the present invention.

FIG. 53 is an axial aberration diagram of an imaging optical systemaccording to Example 12 of the present invention.

FIG. 54 is a lateral aberration diagram of the imaging optical systemaccording to Example 12 of the present invention.

FIG. 55 is a diagram illustrating a structural example of an imagingapparatus according to Example 13 of the present invention.

FIG. 56A is a diagram showing an aspherical shape of a lens surfaceclosest to the image side in the imaging apparatus according to Example13 of the present invention.

FIG. 56B is a diagram showing an aspherical amount of the lens surfaceclosest to the image side of the imaging apparatus according to Example13 of the present invention.

FIG. 57A is a diagram showing a second order differential value of anaspherical surface and a reference spherical surface of the lens surfaceclosest to the image side in the imaging apparatus according to Example13 of the present invention.

FIG. 57B is a diagram showing a second order differential value of anaspherical component of the lens surface closest to the image side inthe imaging apparatus according to Example 13 of the present invention.

FIG. 58 is an axial aberration diagram of an imaging optical systemaccording to Example 13 of the present invention.

FIG. 59 is a lateral aberration diagram of the imaging optical systemaccording to Example 13 of the present invention.

FIG. 60 is a diagram illustrating a structural example of an imagingapparatus according to Example 14 of the present invention.

FIG. 61A is a diagram showing an aspherical shape of a lens surfaceclosest to the object side of the imaging apparatus according to Example14 of the present invention.

FIG. 61B is a diagram showing an aspherical amount of the lens surfaceclosest to the object side of the imaging apparatus according to Example14 of the present invention.

FIG. 62A is a diagram showing a second order differential value of anaspherical surface and a reference spherical surface of the lens surfaceclosest to the object side of the imaging apparatus according to Example14 of the present invention.

FIG. 62B is a diagram showing a second order differential value of anaspherical component of the lens surface closest to the object side ofthe imaging apparatus according to Example 14 of the present invention.

FIG. 63A is a diagram showing of an aspherical shape of a lens surfaceclosest to the image side of the imaging apparatus according to Example14 of the present invention.

FIG. 63B is a diagram showing an aspherical amount of the lens surfaceclosest to the image side of the imaging apparatus according to Example14 of the present invention.

FIG. 64A is a diagram showing a second order differential value of anaspherical surface and a reference spherical surface of the lens surfaceclosest to the image side of the imaging apparatus according to Example14 of the present invention.

FIG. 64B is a diagram showing a second order differential value of anaspherical component of the lens surface closest to the image side ofthe imaging apparatus according to Example 14 of the present invention.

FIG. 65 is an axial aberration diagram of an imaging optical systemaccording to Example 14 of the present invention.

FIG. 66 is a lateral aberration diagram of the imaging optical systemaccording to Example 14 of the present invention.

FIG. 67 is a diagram illustrating a structural example of an imagingapparatus according to Example 15 of the present invention.

FIG. 68A is a diagram showing an aspherical shape of a lens surfaceclosest to the object side of the imaging apparatus according to Example15 of the present invention.

FIG. 68B is a diagram showing an aspherical amount of the lens surfaceclosest to the object side of the imaging apparatus according to Example15 of the present invention.

FIG. 69A is a diagram showing a second order differential value of anaspherical surface and a reference spherical surface of the lens surfaceclosest to the object side of the imaging apparatus according to Example15 of the present invention.

FIG. 69B is a diagram showing a second order differential value of anaspherical component of the lens surface closest to the object side ofthe imaging apparatus according to Example 15 of the present invention.

FIG. 70A is a diagram showing an aspherical shape of a lens surfaceclosest to the image side of the imaging apparatus according to Example15 of the present invention.

FIG. 70B is a diagram showing an aspherical amount of the lens surfaceclosest to the image side of the imaging apparatus according to Example15 of the present invention.

FIG. 71A is a diagram showing a second order differential value of anaspherical surface and a reference spherical surface of the lens surfaceclosest to the image side of the imaging apparatus according to Example15 of the present invention.

FIG. 71B is a diagram showing a second order differential value of anaspherical component of the lens surface closest to the image side ofthe imaging apparatus according to Example 15 of the present invention.

FIG. 72 is an axial aberration diagram of an imaging optical systemaccording to Example 15 of the present invention.

FIG. 73 is a lateral aberration diagram of the imaging optical systemaccording to Example 15 of the present invention.

FIG. 74 is a diagram illustrating of a structural example of an imagingapparatus according to Example 16 of the present invention.

FIG. 75A is a diagram showing an aspherical shape of a lens surfaceclosest to the image side of the imaging apparatus according to Example16 of the present invention.

FIG. 75B is a diagram showing of an aspherical amount of the lenssurface closest to the image side of the imaging apparatus according toExample 16 of the present invention.

FIG. 76A is a diagram showing a second order differential value of anaspherical surface and a reference spherical surface of the lens surfaceclosest to the image side of the imaging apparatus according to Example16 of the present invention.

FIG. 76B is a diagram showing a second order differential value of anaspherical component of the lens surface closest to the image side of,the imaging apparatus according to Example 16 of the present invention.

FIG. 77 is an axial aberration diagram of an imaging optical systemaccording to Example 16 of the present invention.

FIG. 78 is a lateral aberration diagram of the imaging optical systemaccording to Example 16 of the present invention.

FIG. 79 is a diagram illustrating a structural example of an imagingapparatus according to Example 17 of the present invention.

FIG. 80A is a diagram showing a second order differential value of anaspherical surface and a reference spherical surface of a lens surfaceclosest to the object side of the imaging apparatus according to Example17 of the present invention.

FIG. 80B is a diagram showing a second order differential value of anaspherical component of the lens surface closest to the object side ofthe imaging apparatus according to Example 17 of the present invention.

FIG. 81A is a diagram showing a second order differential value of theaspherical surface and the reference spherical surface of the lenssurface closest to the object side of the imaging apparatus according toExample 17 of the present invention.

FIG. 81B is a diagram showing a second order differential value of theaspherical component of the lens surface closest to the object side ofthe imaging apparatus according to Example 17 of the present invention.

FIG. 82 is an axial aberration diagram of an imaging optical systemaccording to Example 17 of the present invention.

FIG. 83 is a lateral aberration diagram of the imaging optical systemaccording to Example 17 of the present invention.

FIG. 84 is an optical path diagram schematically illustrating a mannerin which an image of axial light is formed in the imaging apparatusaccording to the embodiment of the present invention.

FIG. 85 is an optical path diagram schematically illustrating a mannerin which an image of axial light is formed in the imaging apparatusaccording to the embodiment of the present invention.

DESCRIPTION OF THE EMBODIMENTS

A structural example of an imaging apparatus according to an embodimentof the present invention is described.

First, an entire structure of the imaging apparatus is described.

The imaging apparatus of this embodiment includes an imaging opticalsystem including a plurality of lenses, and a curved image plane whichhas a concave surface facing the object side and is disposed in avicinity of an image plane of the imaging optical system, thus beingcapable of correcting a petzval image plane component of the fieldcurvature.

Further, by configuring the imaging optical system as a substantiallypoint symmetry optical system, occurrence of off-axial aberration suchas coma, astigmatism, distortion, and lateral chromatic aberration issuppressed, and hence aberration to be corrected is limited only toaxial aberration such as spherical aberration and axial chromaticaberration.

Making the imaging optical system close to the point symmetry opticalsystem limits a shape of the lens and decreases flexibility in opticaldesign. However, it is more important to obtain an advantage of limitingthe aberration to be corrected only to axial aberration.

Thus, it is possible to realize an imaging apparatus having high imagingperformance with brightness over a wide angle of field.

Therefore, in the imaging apparatus of this embodiment, a focal lengthof the imaging optical system is set substantially equal to a distancefrom an exit pupil to the image plane of the imaging optical system, anda radius of curvature of the image plane is set substantially equal tothe focal length of the imaging optical system. Thus, the imagingoptical system is made close to a point symmetry optical system.

In particular, it is important to adopt a structure in which an opticalsystem closer to the image side than an aperture stop of the imagingoptical system is close to the point symmetry, which is concentric to afield angle light beam.

By setting the focal length of the imaging optical system to besubstantially equal to the distance from the exit pupil to the imageplane of the imaging optical system, it is possible to dispose the imageside principal point and the exit pupil of the imaging optical system atsubstantially the same position.

Because the incident height of the field angle light beam becomes low,the field angle light beam can be handled similarly to the axial light.Thus, it is possible to adopt a structure in which the optical systemcloser to the image side than the aperture stop of the imaging opticalsystem is close to the point symmetry. Specifically, it is preferred tosatisfy the following Expression (1).

Thus, it is possible to appropriately correct off-axial aberration suchas coma, astigmatism, distortion, and lateral chromatic aberration overa wide angle of field.

In addition, by setting the radius of curvature of the image planesubstantially equal to the focal length of the imaging optical system,it is possible to appropriately correct the field curvature.

Specifically, it is preferred to satisfy the following Expression (2).0.8≦f_sys/d_pup≦1.5  (1)0.8≦|R_img|/f_sys≦1.5  (2)

Here, f_sys represents the focal length of the imaging optical system,d_pup represents the distance from the exit pupil to the image plane ofthe imaging optical system, and R_img represents a radius of curvatureof the image plane.

Because the structure of the imaging optical system can appropriatelycorrect astigmatism, the field curvature can be limited only to thepetzval image plane. Because the petzval image plane can be corrected bycurving the image plane, it is possible to suppress the occurrence ofevery off-axial aberration to be small. In other words, it is possibleto limit the remaining aberrations to axial aberrations.

Note that, the image plane of the imaging apparatus as used hereinrefers to a curved image sensor or an optical transmission unit having acurved incident surface.

As the curved image sensor, for example, there are considered an imagesensor formed on a deformable substrate and an element formed of smallplanar image sensors arranged in an array so as to form a concavesurface shape.

In addition, as an optical transmission unit, for example, there isconsidered an image plate which includes optical fibers bound in aplate-like shape and has an end formed into a concave shape and anotherend formed into a flat shape.

Further, it is possible to adopt a structure in which the incidentsurface of the optical transmission unit is curved to have a concavesurface facing the object side to serve as the image plane, and a flatexit plane is connected to the image sensor to serve as the imagingunit.

Next, an action of improving peripheral darkening (darkening at the edgeof the image plane) is described.

In a general imaging optical system, it is known that a peripheral lightintensity ratio drops in accordance with the cosine fourth law withrespect to an angle of field (incident angle) ω. Therefore, theperiphery of the photographed image becomes very dark, and a clear imagecannot be obtained.

In recent years, some digital cameras and digital video camerasremarkably enhance sensitivity at edges so as to digitally correct theperipheral darkening. However, because noise is increased while acontrast remains low, image quality at edges is considerablydeteriorated compared with a center part of the image.

The peripheral darkening causes such a serious problem. This tendency isconspicuous especially in the imaging optical system having a wide angleof field and is one of the factors to be overcome to realize the imagingoptical system having a wide angle of field.

The breakdown of the cosine fourth law of the peripheral light intensityratio is as follows:

-   (a) the square of cos ω due to an increase of an apparent focal    length in accordance with the angle of field;-   (b) the first power of cos ω due to a decrease of an apparent    aperture diameter in accordance with the angle of field; and-   (c) the first power of cos ω due to tightening of the incident angle    to the image plane in accordance with the angle of field.

In the imaging optical system of the imaging apparatus of thisembodiment, the radius of curvature of the image plane is setsubstantially equal to the focal length of the imaging optical system,and hence the apparent focal length can be substantially the same overthe full angle of field.

Thus, the peripheral light intensity ratio corresponding to the squareof cos ω can be improved.

By satisfying Expression (2), it is possible to obtain a reasonableeffect.

In other words, the peripheral light intensity ratio can be improvedfrom the fourth power of cos ω to the square of cos ω. Because theperipheral light intensity ratio of the imaging optical system having awide angle of field can be significantly improved, it is possible toprovide the imaging apparatus that can photograph images having a highcontrast over a wide angle of field, low noise, and high image quality.

Next, the meaning of the above-mentioned Expressions (1) and (2) isdescribed in more detail.

Expression (1) defines the condition for setting the focal length f_sysof the imaging optical system and the distance d_pup from the exit pupilto the image plane of the imaging optical system to be substantiallyequal to each other, and it is possible to adopt a structure in whichthe optical system closer to the image side than the aperture stop ofthe imaging optical system is close to the point symmetry.

If Expression (1) is satisfied, off-axial aberration such as coma,astigmatism, distortion, and lateral chromatic aberration can beappropriately corrected.

If the upper limit of Expression (1) is exceeded, the point symmetry ofthe optical system closer to the image side than the aperture stop ofthe imaging optical system cannot be secured. Then, off-axial aberrationsuch as coma, astigmatism, distortion, and lateral chromatic aberrationoccurs and causes a problem.

If the lower limit of Expression (1) is exceeded, the point symmetry ofthe optical system closer to the image side than the aperture stop ofthe imaging optical system cannot be secured. Then, off-axial aberrationsuch as coma, astigmatism, distortion, and lateral chromatic aberrationoccurs and causes a problem.

Expression (2) defines the condition for setting the radius of curvatureR_img of the image plane and the focal length f_sys of the imagingoptical system to be substantially equal to each other, which is thecondition for appropriately correcting field curvature and astigmatism.

If Expression (2) is satisfied, an image plane shape of the imagingapparatus can be close to the petzval image plane. Therefore, fieldcurvature can be corrected without occurrence of astigmatism over a wideangle of field.

If the upper limit of Expression (2) is exceeded, a difference from thepetzval image plane becomes large at the periphery of the image plane,and hence field curvature occurs so that the imaging performance isdeteriorated.

If the lower limit of Expression (2) is exceeded, a difference from thepetzval image plane becomes large at the periphery of the image plane,and hence field curvature occurs so that the imaging performance isdeteriorated.

If the imaging optical system has a small F value, the depth of focus issmall. Therefore, a permissible range of the field curvature is narrow,and it is necessary to correct the field curvature with high accuracy.

Note that, if the image plane is not a spherical surface but anaspherical surface or a step-like surface, the radius of curvature ofthe image plane is defined as follows.

First, if the shape of the image plane is an aspherical surface, theradius of curvature of a reference spherical surface is regarded as the“radius of curvature of the image plane”. The aspherical surface can beexpressed by an expression α, and the reciprocal of a curvature c on anoptical axis of Expression α is the radius of curvature.

$z = {\frac{{cr}^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}} + {Ar}^{4} + {Br}^{6} + {Cr}^{8} + {Dr}^{10} + {\ldots\mspace{14mu}\alpha}}$

Here, z represents a sag amount (mm) of the aspherical shape in theoptical axis direction, c represents the curvature (1/mm) on the opticalaxis, r represents a distance (mm) from the optical axis in a radialdirection, and A, B, C, and D respectively represent coefficients offourth, sixth, eighth, and tenth orders.

Even if the image plane is an aspherical shape, it is possible todetermine a radius of curvature of a reference curved surface bymeasuring the radius of curvature on the optical axis.

Next, a case where the image plane has a step-like shape is described.

In the case where small image sensors are arrayed or optical fibers arebound to form the curved image plane, the image plane has a step-likeshape in the strict sense.

In this case, the curved surface connecting the center points ofrespective pixels of the image sensors or the center points of therespective optical fibers can be regarded as the image plane.

By calculating the radius of curvature of the reference curved surfacefrom a result of fitting the curved surface with the above-mentionedexpression α by the least square method, it is possible to determine theradius of curvature of the image plane.

In addition, the imaging apparatus of this embodiment adjusts thein-focus position by changing an interval between the imaging opticalsystem and the image plane.

FIGS. 13A and 13B illustrate an imaging relationship when an objectplane is disposed at a finite distance.

In FIG. 13A, OBJ represents the object plane, SYS represents the imagingoptical system, and IMG represents the image plane. The imaging opticalsystem SYS forms an image of an object point on the object plane OBJ atan image point on the image plane IMG.

As illustrated in FIG. 13A, because the imaging optical system SYS formsthe image of the object point at the same distance from the imagingoptical system SYS on the petzval image plane, the object plane OBJ inthis case becomes a curved shape.

However, it is preferred in the imaging optical system that the objectplane OBJ be a flat surface.

As illustrated in FIG. 13B, object points disposed apart from theoptical axis are not positioned on the curved object plane illustratedby a broken line but on a flat object plane illustrated by a solid line.Then, as illustrated by an arrow A of FIG. 13B, the object point movesin the direction apart from the imaging optical system SYS, and theimage point also moves, as illustrated by an arrow B, from the petzvalimage plane illustrated by a broken line to the image plane IMGillustrated by a solid line in the direction approaching the imagingoptical system SYS.

This movement amount on the image plane side is regarded as a defocusamount in a traveling direction of a light beam, and an example in amodel of the imaging optical system of FIG. 13B is shown in FIG. 14 as agraph.

FIG. 14 shows a relationship between the in-focus position and the shapeof the image plane when focus adjustment is performed in an example.

In this example, parameters are set so that the focal length of theimaging optical system is f_sys=12.0 (mm), the radius of curvature ofthe image plane is R_img=12.0 (mm), the distance from the exit pupil tothe image plane of the imaging optical system is d_pup=12.0 (mm), theobject distance is S=−300 (mm), and the angle of field is ω=60(degrees).

As described above, if the object plane is a flat surface, the in-focusposition of each field angle light beam is defocused from the petzvalimage plane toward the imaging optical system side.

The defocus amount of the light beam in the traveling direction is shownin the graph of the in-focus position by a solid line.

In addition, the radius of curvature of the image plane is setsubstantially equal to the focal length of the imaging optical system,which corresponds to the petzval image plane shape with the objectdistance of infinity.

It should be understood that the in-focus position shown by solid lineand the image plane shape shown by dots correspond to each other at theobject distance of infinity. However, FIG. 14 shows that the in-focusposition and the image plane shape correspond to each other preciselyeven in the case where the object distance is decreased to S=−300 (mm).

This means that the focus adjustment of the flat object plane can beperformed without occurrence of field curvature in any object distancefrom infinity to S=−300 (mm).

In addition, the above-mentioned coincidence between the in-focusposition and the image plane shape can be realized in a wide range ofangle of field of −60 to +60 (degrees).

The focal length of the imaging optical system is set substantiallyequal to the distance from the exit pupil to the image plane of theimaging optical system, and the radius of curvature of the image planeis set substantially equal to the focal length of the imaging opticalsystem. Then, the focus adjustment can be performed only by changing thedistance between the imaging optical system and the image plane withoutchanging the image plane shape.

For this purpose, it is necessary to satisfy Expressions (1) and (2).

Because the imaging optical system having a very small F value such asthe imaging apparatus of this embodiment described above has a verysmall depth of focus, it is significantly important for the imagingapparatus that the focus adjustment with high accuracy can be easilyrealized.

(First Embodiment)

In this embodiment, in an imaging optical system, power of an opticalsystem closer to the object side than an aperture stop and power of anoptical system closer to the image side than the aperture stop arepositive powers different from each other. Thus, it is possible tosuppress aberration of a particularly high order so as to obtain highimaging performance.

Power arrangement of the imaging optical system is described in moredetail.

In the imaging optical system of a recent imaging apparatus, aretrofocus type lens is common. The retrofocus type lens includes anoptical system having negative power disposed closer to the object sidethan the aperture stop and an optical system having positive powerdisposed closer to the image side than the aperture stop.

In this structure, the optical systems in front of and behind theaperture stop have relatively strong negative power and relativelystrong positive power compared with positive power necessary for theentire imaging optical system, and this structure gives power largerthan necessary so as to cause large aberration. Therefore, there is aproblem in that aberration is apt to cause particularly in higher order.

In addition, because the imaging optical system is not a point symmetrystructure, off-axial aberration occurs greatly.

In contrast, in the imaging optical system of this embodiment, both theoptical system closer to the object side than the aperture stop and theoptical system closer to the image side than the aperture stop havepositive power.

Therefore, compared with the positive power necessary for the entireimaging optical system, relatively small power can be given to theoptical systems in front of and behind the aperture stop. Thus,occurrence of aberration can be suppressed.

In particular, because high order aberration can be suppressed, thestructure can easily obtain high imaging performance.

In addition, because the structure is close to a point symmetrystructure, occurrence of off-axial aberration is suppressed, and hencehigh imaging performance can be realized over a wide angle of field.

Further, in the imaging optical system of the imaging apparatus of thisembodiment, the power of the optical system closer to the object sidethan the aperture stop is different from the power of the optical systemcloser to the image side than the aperture stop. Therefore, flexibilityin optical design can be enhanced.

In particular, by setting the power of the optical system closer to theobject side than the aperture stop to be smaller than the power of theoptical system closer to the image side than the aperture stop, it ispossible to obtain an advantage that axial aberration can be easilycorrected.

Specifically, it is preferred to satisfy Expression (3):0<φ_fro<φ_beh  (3),where φ_fro represents the power of the optical system closer to theobject side than the aperture stop, and φ_beh represents the power ofthe optical system closer to the image side than the aperture stop.

The spherical aberration and the axial chromatic aberration havetendency to be vulnerable to the influence of power of a surface havinga high incident height h (surface having a large light beam width).

According to a third order aberration coefficient, spherical aberrationoccurs greatly in proportion to the fourth power of the incident heighth, and the axial chromatic aberration occurs greatly in proportion tothe square of the incident height h. In addition, high order sphericalaberration occurs greatly in a surface in which the light beam widthoccupies a large ratio to the radius of curvature.

In the imaging optical system of this embodiment, both the opticalsystem closer to the object side than the aperture stop and the opticalsystem closer to the image side than the aperture stop have positivepower. Thus, the imaging optical system of this embodiment has a featurethat the optical system closer to the object side than the aperture stophas a large light beam width on each lens surface and that the opticalsystem closer to the image side than the aperture stop has a small lightbeam width on each lens surface.

Therefore, the power of the optical system closer to the object sidethan the aperture stop is reduced so that the optical system closer tothe image side than the aperture stop shares the power. Thus, sphericalaberration and axial chromatic aberration generated in the opticalsystem closer to the object side than the aperture stop is suppressed tobe small and can be corrected easily by the optical system closer to theimage side than the aperture stop.

In addition, because high order spherical aberration generated in theoptical system closer to the object side than the aperture stop can alsobe suppressed to be small, spherical aberration can be appropriatelycorrected also at an F value smaller than F/2.0.

When the high order spherical aberration is appropriately corrected,chromatic spherical aberration can be easily corrected, and this is animportant factor for realizing high imaging performance.

Thus, it is possible to realize the imaging optical system having asmall F value and high imaging performance over a wide angle of field.Using this imaging optical system having a small F value and highimaging performance, it is possible to realize an imaging apparatushaving high resolution.

Next, the size of the imaging optical system is described.

If the optical system closer to the object side than the aperture stophas negative power and the optical system closer to the image side thanthe aperture stop has positive power, which constitute a retrofocustype, the entire length of the imaging optical system becomes long.

On the other hand, in the imaging optical system of the imagingapparatus of this embodiment, both the power of the optical systemcloser to the object side than the aperture stop and the power of theoptical system closer to the image side than the aperture stop are setto positive power.

When the optical systems on the object side and on the image side of theaperture stop are set to have positive powers, power necessary for theentire optical system can be obtained without a power loss. Thus, theimaging optical system can be compact.

Specific examples of this embodiment are hereinafter described.

Example 1

An imaging optical system used for an imaging apparatus of this exampleincludes an aperture stop and four lenses as illustrated in FIG. 1.

The imaging optical system includes, in order from the object side: afirst lens G1 as a meniscus lens having a convex surface facing theobject side; a second lens G2 as a plano-convex lens having a convexsurface facing the object side; an aperture stop STO; a third lens G3 asa plano-convex lens having a convex surface facing the image side; and afourth lens G4 as a meniscus lens having a convex surface facing theimage side.

An exit surface of the first lens G1 is cemented to an incident surfaceof the second lens G2, an exit surface of the second lens G2 is cementedto an incident surface of the third lens G3, and an exit surface of thethird lens G3 is cemented to an incident surface of the fourth lens G4.

The aperture stop STO is constituted by a light blocking member disposedon the cemented surface between the exit surface of the second lens G2and the incident surface of the third lens G3.

In addition, IMG in FIG. 1 represents an image plane.

As illustrated in FIG. 1, the image plane IMG of an image sensor has aspherically curved shape, which is placed along a field curvature of theimaging optical system. Thus, good imaging performance is realized overthe entire image plane IMG.

Table 1 shows a structure of the imaging apparatus of this example.

Surface number 1 is an incident surface of the first lens G1, surfacenumber 2 is a cemented surface between an exit surface of the first lensG1 and an incident surface of the second lens G2, and surface number 3is the cemented surface between the exit surface of the second lens G2and the incident surface of the third lens G3, which is an aperture stopsurface STO.

Surface number 4 is a cemented surface between the exit surface of thethird lens G3 and the incident surface of the fourth lens G4, surfacenumber 5 is an exit surface of the fourth lens G4, and surface number 6is the image plane IMG of the image sensor.

Further, R represents a radius of curvature (mm), d represents a surfaceinterval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number.

TABLE 1 Surface number R D Nd νd 1 3.1178 2.2559 1.902000 25.1 2 1.02480.8652 1.850259 32.3 3 (STO) Infinity 1.0230 1.850259 32.3 4 −1.11112.0263 1.922860 18.9 5 −2.9693 0.5323 6 (IMG) −3.5534

A refractive index Nd2=1.850259 of the second lens G2 is set smallerthan a refractive index Nd1=1.902000 of the first lens G1, and thecemented surface between the exit surface of the first lens G1 and theincident surface of the second lens G2 is formed as a lens surfacehaving a convex shape facing the object side so as to have negativepower.

A refractive index Nd4=1.922860 of the fourth lens G4 is set larger thana refractive index Nd3=1.850259 of the third lens G3, and the cementedsurface between the exit surface of the third lens G3 and the incidentsurface of the fourth lens G4 is formed as a lens surface having aconvex shape facing the image side so as to have negative power.

In the imaging apparatus of this example, by these two lens surfaceshaving negative power, spherical aberration, axial chromatic aberration,chromatic spherical aberration, and the like generated on the incidentsurface of the first lens G1 and the exit surface of the fourth lens G4are appropriately corrected.

In addition, Table 2 shows the specifications of the imaging apparatusof this example.

TABLE 2 Focal length of f_sys 3.600 (mm) imaging optical system F valueF/# 1.20 Angle of field 2ω 120.0 (deg) Entire length L_sys 6.170 (mm)Distance from exit d_pup 3.666 (mm) pupil to image plane

The imaging apparatus of this example has a very small F value of F/1.2and a very wide angle of field of 120.0 (degrees), and still has a smallentire length of 6.170 (mm), which is an example of the imagingapparatus realizing brightness, high resolution, a very wide angle offield, and a compact size, at the same time.

Table 3 shows values of Expressions (1), (2), and (4) in the imagingapparatus of this example.

TABLE 3 Conditional f_sys/d_pup 0.98 expression (1) Conditional|R_img|/f_sys 0.94 expression (2) Conditional |R_img|/d_pup 0.93expression (4)

The value of Expression (1) is 0.98, which satisfies the range ofExpression (1). Thus, good optical performance can be obtained over awide angle of field.

The value of Expression (2) is 0.94, which satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a very wide angle of field of 120.0(degrees).

The following Expression (4) defines the condition for setting theradius of curvature R_img of the image plane to be substantially equalto the distance d_pup from the exit pupil to the image plane of theimaging optical system.0.8≦|R_img|/d_pup≦1.5  (4)

If Expression (4) is satisfied, the imaging optical system can have astructure closer to point symmetry.

In the imaging apparatus of this example, the distance between theimaging optical system and the image plane is changed so as to performfocus adjustment.

In this case, if Expression (4) is satisfied, it is possible to suppressfield curvature due to focus adjustment to be very small at an objectdistance in a wide range from infinity to a very close distance, andhence high resolution photography can be performed.

If the value falls below the lower limit of Expression (4), or if thevalue exceeds the upper limit of Expression (4), a difference from thestructure in which the optical system closer to the image side than theaperture stop of the imaging apparatus is close to a point symmetry,that is, a difference from the structure close to concentric withrespect to the field angle light beam becomes large. As a result,off-axial aberration occurs greatly and causes a problem. In addition,along with a variation of a subject distance, field curvature occurs andcauses a problem.

The value of Expression (4) is 0.93, which satisfies the range ofExpression (4).

In addition, in the imaging apparatus of this example, the focal lengthof the imaging optical system is set substantially equal to the distancefrom the exit pupil to the image plane of the imaging optical system.

Table 4 shows values of power φ_fro of the optical system closer to theobject side than the aperture stop STO and power φ_beh of the opticalsystem closer to the image side than the aperture stop STO, Expression(3), and a power ratio φ_beh/φ_fro in the imaging apparatus of thisexample.

TABLE 4 Power of optical system closer to φ_fro 0.25614 (1/mm) objectside than aperture stop Power of optical system closer to φ_beh 0.26686(1/mm) image side than aperture stop Conditional 0 < φ_fro < φ_behSatisfied expression (3) Power ratio φ_beh/φ_fro 1.04

The power φ_fro of the optical system closer to the object side than theaperture stop STO is set different from the power φ_beh of the opticalsystem closer to the image side than the aperture stop STO. Thus,compared with a conventional ball lens, flexibility of aberrationcorrection is high, and ability of correcting spherical aberration oraxial chromatic aberration is improved.

In particular, the power φ_fro of the optical system closer to theobject side than the aperture stop STO is set smaller than the powerφ_beh of the optical system closer to the image side than the aperturestop STO, and hence spherical aberration can be appropriately corrected.

Specifically, as shown in Table 3, the imaging apparatus of this exampleis structured to satisfy Expression (3).

In other words, both the optical system closer to the object side thanthe aperture stop STO and the optical system closer to the image sidethan the aperture stop STO have positive power, and the power of theoptical system closer to the image side than the aperture stop STO isset 1.04 times larger than the power of the optical system closer to theobject side than the aperture stop.

Therefore, the ability of correcting spherical aberration or axialchromatic aberration is improved, and high imaging performance can beobtained even at a small F value of F/1.2.

In addition, in the imaging apparatus of this example, curvature centersof all lens surfaces are disposed closer to the aperture stop than thepositions of the lens surfaces so as to form concentric shapes withrespect to the aperture stop.

However, the third surface is a flat plane, which is not regarded as alens surface because the surfaces in front of and behind the thirdsurface have the same refractive index.

In this way, the imaging apparatus has a structure close to pointsymmetry, and an incident angle of the field angle light beam to eachlens surface can be close to an incident angle of the axial light toeach lens surface.

Thus, it is possible to suppress occurrence of off-axial aberration, andaxial aberration is appropriately corrected so as to realize the imagingapparatus that can perform good aberration correction in a wide range ofthe angle of field.

FIG. 2 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 3 illustrates a lateral aberrationdiagram thereof.

As illustrated in FIG. 2, spherical aberration, axial chromaticaberration, astigmatism, field curvature, distortion, and chromaticspherical aberration are appropriately corrected. Here, chromaticspherical aberration is defined as a difference between a sphericalaberration amount of a reference wavelength (for example, d-line) and aspherical aberration amount of each wavelength (for example, C-line,F-line, g-line, or the like).

In a bright optical system, high order spherical aberration is apt tooccur, which has a tendency to be spherical aberration that rolls in apart having a large incident height.

The imaging apparatus of the example is a very bright optical systemhaving F/1.2 and suppresses the rolling of spherical aberration in thepart having a large incident height by the effect of this embodiment soas to realize an upright spherical aberration shape.

In this way, light beams at individual incident heights are condensed ina vicinity of the image plane. In particular, the spherical aberrationshape is controlled so that light rays in a low part close to zeropercent of the incident height are condensed a little back from theimage plane and that light rays in a part higher than 50 percent of theincident height are condensed on the image plane.

In this way, light rays in the part having a large incident height arecondensed on the image plane in a concentrated manner so as to suppressbroadening of a spot diagram, and hence high imaging performance isrealized.

As described above, using the effect of this embodiment, even if theimaging optical systems are different between the object side and theimage side of the aperture stop, the structure on the image side of theaperture stop can be close to point symmetry.

In particular, when Expressions (2) and (4) are satisfied, occurrence ofoff-axial aberration such as coma, field curvature, distortion, andlateral chromatic aberration can be suppressed. Because the aberrationcan be limited only to axial aberration such as spherical aberration andaxial chromatic aberration, the ability of correcting aberration can besignificantly improved.

Therefore, it is possible to realize the imaging optical system capableof appropriately correcting aberration even in a very wide angle offield and a very small F value smaller than F/2.0, such as the imagingoptical system of this example.

Further, because the above-mentioned imaging optical system can berealized in a simple lens structure, it is possible to reduce the sizeof the imaging optical system.

One of features of this example is that the imaging optical system is a“bright optical system”.

Because the bright optical system can receive a large amount of light atone time, there are advantages that exposure time can be shortened, andthat blur due to shaking, image blur due to movement of the object,noise, and the like can be reduced.

The received light amount increases in inverse proportion to the squareof the F value. Therefore, with respect to a general optical system ofF/3.5, the bright optical system of F/2.0 can receive approximately 3.1times of light amount, and the bright optical system of F/1.2 accordingto this example can receive approximately 8.5 times of light amount.

In other words, using the imaging apparatus of this example, blur due toshaking, image blur due to movement of the object, and noise can bereduced to approximately 1/8.5, and hence an image with very high imagequality can be taken.

Next, the peripheral light intensity ratio is described.

In a general imaging optical system, the peripheral light intensityratio drops in accordance with the cosine fourth law. Therefore, thedrop of the peripheral light intensity ratio is a large problem in theimaging optical system having a wide angle of field.

In the case of this example, the angle of field is 2ω=120 degrees and ahalf angle of field is ω=60 degrees. The peripheral light intensityratio at an angle of field of ω=60 degrees is cos ω^4=0.0625, and only6% of light amount on the optical axis reaches the periphery of theimage sensor.

Therefore, the periphery of the photographed image becomes very dark,and hence a clear image cannot be obtained.

In recent years, some digital cameras and digital video camerasremarkably enhance sensitivity in the periphery so as to digitallycorrect peripheral darkening. However, because the SNR cannot bechanged, noise becomes conspicuous, and image quality in the peripheryis significantly deteriorated compared with that in the center portion.

The considerably small decrease of the peripheral light intensity ratiocauses such a serious problem.

In contrast, the imaging optical system of this example exerts theeffect on the peripheral darkening, too.

Because the focal length of each angle of field can be substantiallyequal to the focal length on the optical axis by satisfying Expression(2), peripheral light intensity can be increased by the square of cos ω.

Because the incident angle can be substantially orthogonal to the imagesensor plane by satisfying Expression (3), the peripheral lightintensity can be increased by the first power of cos ω.

Further, because the peripheral light intensity can be increased by thethird power of cos ω by satisfying Expressions (4) and (3) at the sametime, the peripheral light intensity ratio can be proportional to thefirst power of cos ω.

Therefore, the imaging optical system of this example has a very wideangle of field of 2ω=120 degrees and still can permit 50% of lightamount on the optical axis to reach the periphery of the image sensorbecause the peripheral light intensity ratio is cos¹ ω=0.0500. Thislight amount is eight times larger than that of a general wide angleimaging optical system described above and there is an advantage ofsuppressing the peripheral darkening to be very small.

Thus, because it is possible to prevent the periphery of the image frombeing too dark, a sufficient contrast can be obtained even in theperiphery.

In addition, it is possible to generate inconspicuous noise even in thecase where sensitivity in the periphery is remarkably enhanced so as todigitally correct the peripheral darkening in the digital camera or thedigital video camera.

In addition, in order to realize high resolution in the color imagingapparatus for taking images of a plurality of wavelengths, it isimportant to appropriately correct chromatic aberration.

Because the imaging optical system of this example satisfies Expressions(2) and (4), the structure suppresses lateral chromatic aberration asoff-axial aberration. Because the target of correcting chromaticaberration is limited to axial chromatic aberration and chromaticspherical aberration as axial aberration, the ability of correctingchromatic aberration is improved.

In correcting the axial chromatic aberration, it is important tounderstand features of the aberration. Axial chromatic aberration andchromatic spherical aberration are both affected more significantly bypower of the lens surface as the paraxial incident height to the lenssurface is higher.

According to the third order aberration theory, axial chromaticaberration is proportional to the square of the paraxial incident heighton the lens surface, and chromatic spherical aberration is proportionalto the fourth power of the paraxial incident height on the lens surface.

In particular, because the chromatic spherical aberration issignificantly affected by the incident height on the lens surface, it ispreferred to reduce influence on chromatic aberration of the opticalsystem closer to the object side than the aperture stop having a largeincident height on the lens surface, and to increase influence onchromatic aberration of the optical system closer to the image side thanthe aperture stop so as to correct chromatic aberration.

With this structure, even in a bright optical system, it is possible tosuppress occurrence of high order chromatic spherical aberration in theoptical system closer to the object side than the aperture stop, and theoptical system closer to the image side than the aperture stop cancorrect chromatic spherical aberration to be set close to zero (imageplane) at a position having a large incident height.

Thus, it is possible to suppress the broadening of the spot diagram ofeach wavelength and realize high imaging performance.

Therefore, the power of the optical system closer to the object sidethan the aperture stop is set weaker than the power of the opticalsystem closer to the image side than the aperture stop, and henceinfluence of the optical system closer to the object side than theaperture stop on chromatic aberration is suppressed to be small.

Further, in the imaging optical system of this example, an Abbe numberof the lens closest to the object side is set larger than an Abbe numberof the lens closest to the image side.

Specifically, the first lens, which is the lens disposed closest to theobject side, has an Abbe number νd_most_obj=25.1, and the fourth lens,which is the lens disposed closest to the image side, has an Abbe numberνd_most_img=18.9 so that the following Expression (5) is satisfied.νd_most_img<νd_most_obj  (5)

In this way, influence of the first lens which is the lens disposedclosest to the object side on chromatic aberration on the incidentsurface is reduced, and hence occurrence of axial chromatic aberrationor chromatic spherical aberration is suppressed.

Therefore, axial chromatic aberration and chromatic spherical aberrationcan be easily corrected.

In addition, the influence on chromatic aberration is reduced also onthe exit surface of the first lens.

For this reason, a difference between an Abbe number of a lens of theimaging optical system closest to the image side and an Abbe number of alens of the imaging optical system adjacent to the lens in the imagingapparatus is set larger than a difference between an Abbe number of alens of the imaging optical system closest to the object side and anAbbe number of a lens adjacent to the lens.

Specifically, an absolute value of a difference between an Abbe numberνd_most_img=18.9 of the fourth lens which is the lens disposed closestto the image side and an Abbe number νd_next_img=32.3 of a lens adjacentto the fourth lens is |Δνd_most_img|=13.4, while an absolute value of adifference between an Abbe number νd_most_obj=25.1 of the first lenswhich is the lens disposed closest to the object side and an Abbe numberνd_next_obj=32.3 of a lens adjacent to the first lens is|Δνd_most_obj|=7.2, and hence the following Expression (6) is satisfied.|Δνd_most_img|>|Δνd_most_obj|  (6)

In this way, on the object side of the aperture stop in which the lightbeam width is large, the influence on chromatic aberration is reduced,and hence occurrence of chromatic aberration, particularly axialchromatic aberration and chromatic spherical aberration is suppressed tobe small. Further, on the image side of the aperture stop in which thelight beam width is small, influence on chromatic aberration isenhanced. Thus, axial chromatic aberration and chromatic sphericalaberration are appropriately corrected.

With this structure, spherical aberration of each wavelength in aposition of high incident height is set close to zero (image plane), andhence high imaging performance is realized, in which the broadening of aspot diagram of each wavelength is suppressed.

Example 2

An imaging optical system used for an imaging apparatus of this exampleincludes an aperture stop and four lenses as illustrated in FIG. 4.

The imaging optical system includes, in order from the object side: afirst lens G1 as a meniscus lens having a convex surface facing theobject side; a second lens G2 as a plano-convex lens having a convexsurface facing the object side; an aperture stop STO; a third lens G3 asa plano-convex lens having a convex surface facing the image side; and afourth lens G4 as a meniscus lens having a convex surface facing theimage side.

An exit surface of the first lens G1 is cemented to an incident surfaceof the second lens G2, an exit surface of the second lens G2 is cementedto an incident surface of the third lens G3, and an exit surface of thethird lens G3 is cemented to an incident surface of the fourth lens G4.

The aperture stop STO is constituted by a light blocking member disposedon the cemented surface between the exit surface of the second lens G2and the incident surface of the third lens G3.

IMG in FIG. 4 represents an image plane and is an incident surface of anoptical transmission unit OTM.

The optical transmission unit OTM of this example is an image fiberformed of bound optical fibers of a few micron pitch and has a role oftransmitting an image formed on the image plane of the imaging opticalsystem to an image sensor ICD.

The incident surface of the optical transmission unit OTM has aspherically curved shape, and the exit surface is a flat surface havingintimate contact with the image sensor ICD for connection. Thus, animage sensor unit ICU is constituted.

The incident surface shape of the optical transmission unit OTM isformed along the field curvature of the imaging optical system so as torealize good image formation over the entire region of the image planeIMG.

The optical transmission unit OTM is used in this example. In contrastto a structure in which the image sensor itself has a spherical surface,there is an advantage of easy production of the imaging unit ICU inwhich one surface of the optical transmission unit OTM has a sphericalsurface while the other surface is connected to the image sensor ICD.

Table 5 shows a structure of the imaging apparatus of this example.

Surface number 1 is an incident surface of the first lens G1, surfacenumber 2 is a cemented surface between an exit surface of the first lensG1 and an incident surface of the second lens G2, and surface number isa cemented surface between the exit surface of the second lens G2 andthe incident surface of the third lens G3, which is an aperture stopsurface STO.

Surface number 4 is a cemented surface between the exit surface of thethird lens G3 and the incident surface of the fourth lens G4, surfacenumber 5 is an exit surface of the fourth lens G4, and surface number 6is the image plane IMG, which is an incident surface of the opticaltransmission unit OTM of the imaging unit ICU. Further, the exit surfaceof the optical transmission unit OTM is connected to the image sensorICD.

In Table 5, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number.

TABLE 5 Surface number R D Nd νd 1 3.3929 1.9894 2.102000 16.8 2 1.27821.6473 2.000600 25.5 3 (STO) Infinity 1.2244 2.000600 25.5 4 −1.10671.8419 2.102000 16.8 5 −2.8685 0.3207 6 (IMG) −3.3496

A refractive index Nd2=2.000600 of the second lens G2 is set smallerthan a refractive index Nd1=2.102000 of the first lens G1, and thecemented surface between the exit surface of the first lens G1 and theincident surface of the second lens G2 is formed as a lens surfacehaving a convex shape facing the object side so as to have negativepower.

A refractive index Nd4=2.102000 of the fourth lens G4 is set larger thana refractive index Nd3=2.000600 of the third lens G3, and the cementedsurface between the exit surface of the third lens G3 and the incidentsurface of the fourth lens G4 is formed as a lens surface having aconvex shape facing the image side so as to have negative power.

In the imaging apparatus of this embodiment, by these two lens surfaceshaving negative power, spherical aberration, axial chromatic aberration,chromatic spherical aberration, and the like generated on the incidentsurface of the first lens G1 and the exit surface of the fourth lens G4are appropriately corrected.

In addition, Table 6 shows the specifications of the imaging apparatusof this example.

TABLE 6 Focal length of f_sys 3.600 (mm) imaging optical system F valueF/# 1.00 Angle of field 2ω 120.0 (deg) Entire length L_sys 6.703 (mm)Distance from exit d_pup 3.624 (mm) pupil to image plane

The imaging apparatus of this example has a F value of F/1.0, which iseven smaller than that in the imaging apparatus of Example 1, and a verywide angle of field of 120.0 (degrees), and still has a small entirelength of 6.703 (mm), which is an example of the imaging apparatusrealizing brightness, high resolution, a very wide angle of field, and acompact size, at the same time.

Table 7 shows values of Expressions (1), (2), and (4) in the imagingapparatus of this example.

TABLE 7 Conditional f_sys/d_pup 0.99 expression (1) Conditional|R_img|/f_sys 0.93 expression (2) Conditional |R_img|/d_pup 0.92expression (4)

The value of Expression (1) is 0.99, which satisfies the range ofExpression (1).

The value of Expression (2) is 0.93, which satisfies the range ofExpression (2).

Thus, field curvature and astigmatism can be appropriately correctedover a very wide angle of field of 120.0 (degrees).

The value of Expression (4) is 0.92, which satisfies the range ofExpression (4).

Thus, good optical performance can be obtained over a wide angle offield.

FIG. 5 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 6 illustrates a lateral aberrationdiagram thereof.

Table 8 shows values of power φ_fro of the optical system closer to theobject side than the aperture stop STO and power φ_beh of the opticalsystem closer to the image side than the aperture stop STO, Expression(3), and a power ratio φ_beh/φ_fro in the imaging apparatus of thisexample.

TABLE 8 Power of optical system closer φ_fro 0.26989 (1/mm) to objectside than aperture stop Power of optical system closer φ_beh 0.32343(1/mm) to image side than aperture stop Conditional 0 < φ_fro < φ_behSatisfied expression (3) Power ratio φ_beh/φ_fro 1.20

The power φ_fro of the optical system closer to the object side than theaperture stop STO is set different from the power φ_beh of the opticalsystem closer to the image side than the aperture stop STO. Thus,compared with a conventional ball lens, flexibility of aberrationcorrection is high, and ability of correcting spherical aberration oraxial chromatic aberration is improved.

In particular, the power φ_fro of the optical system closer to theobject side than the aperture stop STO is set smaller than the powerφ_beh of the optical system closer to the image side than the aperturestop STO, and hence spherical aberration can be appropriately corrected.

Specifically, as shown in Table 8, the imaging apparatus of this exampleis structured to satisfy Expression (3).

Further, the structure satisfies the following Expression (7), and hencethe effect of this embodiment can be sufficiently obtained.φ_beh/φ_fro≧1.1  (7)

In other words, both the optical system closer to the object side thanthe aperture stop STO and the optical system closer to the image sidethan the aperture stop STO have positive power, and the power of theoptical system closer to the image side than the aperture stop STO isset approximately 20% larger than the power of the optical system closerto the object side than the aperture stop. Therefore, the ability ofcorrecting spherical aberration or axial chromatic aberration isimproved, and high imaging performance can be obtained even in a verysmall F value of F/1.0.

In addition, in the imaging apparatus of this example, curvature centersof all lens surfaces are disposed closer to the aperture stop than thepositions of the lens surfaces so as to form concentric shapes withrespect to the aperture stop.

However, the third surface is a flat plane, which is not regarded as alens surface because the surfaces in front of and behind the thirdsurface have the same refractive index.

In this way, the imaging apparatus has a structure close to pointsymmetry, and an incident angle of the field angle light beam to eachlens surface can be close to an incident angle of the axial light toeach lens surface.

Thus, it is possible to suppress occurrence of off-axial aberration, andaxial aberration is appropriately corrected so as to realize the imagingapparatus that can perform good aberration correction in a wide range ofthe angle of field.

In addition, in the imaging apparatus of this example, as shown in Table5, the refractive index of the first lens G1 and the fourth lens G4 isNd=2.102000, and the refractive index of the second lens G2 and thethird lens G3 is Nd=2.000600, which are high refractive indexes.

Power φs of a lens surface is given by the following expression:φs=(N′−N)/R  (8),where N represents a refractive index of the lens surface on the objectside, N′ represents a refractive index of the lens surface on the imageside, and R represents a radius of curvature of the lens surface.

As to the incident surface of the lens closest to the object side in theimaging optical system of the imaging apparatus, there is air on theobject side of the incident surface, and N in Expression (7) isN=1.000000.

N′ in Expression (8) is the refractive index of the lens closest to theobject side. If the refractive index is set higher, the radius ofcurvature R for obtaining the same lens surface power φs can be setlarger. In other words, if the refractive index of the lens closest tothe object side is set higher, the radius of curvature of the incidentsurface can be set larger, and there is the effect that occurrence ofspherical aberration is suppressed and that good imaging performance canbe easily obtained.

It is preferred to set the refractive index of the lens closest to theobject side in the imaging apparatus to be a high refractive index, andit is preferred to satisfy Expression (9).1.850000≦Nd≦2.300000  (9)

If the lower limit value of Expression (9) is exceeded, the radius ofcurvature of the incident surface of the lens closest to the object sidebecomes small. Then, spherical aberration occurs greatly and causes aproblem.

If the upper limit value of Expression (9) is exceeded, the radius ofcurvature of the incident surface of the lens closest to the object sidebecomes large. Then, it is necessary to secure a large distance from theincident surface to the aperture stop, which causes a problem in thatthe size of the imaging apparatus is increased.

Similarly, it is preferred to set the refractive index of the lensclosest to the image side in the imaging apparatus to be a highrefractive index, and it is preferred to satisfy Expression (7).

The refractive index of the lens closest to the object side is sethigher than the refractive index of the adjacent lens, and the exitsurface of the lens closest to the object side has negative power so asto correct spherical aberration. In addition, the Abbe number of thelens closest to the object side is set lower than the Abbe number of theadjacent lens so as to correct chromatic aberration.

Similarly, the refractive index of the lens closest to the image side isset higher than the refractive index of the adjacent lens, and theincident surface of the lens closest to the image side has negativepower so as to correct spherical aberration. In addition, the Abbenumber of the lens closest to the image side is set lower than the Abbenumber of the adjacent lens so as to correct chromatic aberration.

In this way, using this embodiment, it is possible to realize theimaging apparatus having a wide angle of field and high resolution.

Example 3

The imaging optical system used for the imaging apparatus of thisexample includes an aperture stop and five lenses as illustrated in FIG.7.

The imaging optical system includes, in order from the object side: afirst lens G1 as a meniscus lens having a convex surface facing theobject side; a second lens G2 as a meniscus lens having a convex surfacefacing the object side; a third lens G3 as a meniscus lens having aconvex surface facing the object side; an aperture stop STO; a fourthlens G4 as a biconvex lens having a convex surface facing the imageside; and a fifth lens G5 as a meniscus lens having a convex surfacefacing the image side.

The first lens G1 is cemented to the second lens G2, the second lens G2is cemented to the third lens G3, and the fourth lens G4 is cemented tothe fifth lens G5.

The aperture stop STO of the imaging apparatus of this example isdisposed in an air layer between the third lens and the fourth lens, anda variable aperture stop can be disposed.

The variable aperture stop enables adjustment of brightness and controlof depth of focus.

In an imaging apparatus having a small F value as in this example, thedepth of focus becomes shallow. Therefore, it is required to control thedepth of focus by the aperture stop.

When the aperture stop STO is disposed in the air layer, it is difficultto correct aberration. However, there is significant meaning indisposing the variable aperture stop in the imaging apparatus, and themethod of correcting aberration when the aperture stop STO is disposedin the air layer is one of the important subjects.

In addition, the same imaging unit ICU as that in Example 2 is used.

Table 9 shows a structure of the imaging apparatus of this example.

Surface number 1 is an incident surface of the first lens G1, surfacenumber 2 is a cemented surface between an exit surface of the first lensG1 and an incident surface of the second lens G2, surface number 3 is acemented surface between the exit surface of the second lens G2 and anincident surface of the third lens G3, and surface number 4 is anincident surface of the third lens G3, which is connected to the airlayer.

Surface number 5 is the aperture stop STO, which is disposed in the airlayer. Surface number 6 is the incident surface of the fourth lens G4,surface number 7 is the cemented surface between the exit surface of thefourth lens G4 and the incident surface of the fifth lens G5, andsurface number 8 is the exit surface of the fifth lens G5.

Surface number 9 is the image plane IMG, which is the incident surfaceof the optical transmission unit OTM of the imaging unit ICU. Further,the exit surface of the optical transmission unit OTM is connected tothe image sensor ICD.

In Table 9, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number.

TABLE 9 Surface number R D Nd νd 1 9.2950 2.3612 2.001100 23.6 2 5.03293.2825 1.726350 26.1 3 7.6974 1.4531 1.670939 55.7 4 43.5438 0.6507 5(STO) Infinity 0.5000 6 25.3784 4.2148 1.882997 40.8 7 −4.6940 5.49672.000800 25.0 8 −12.3234 4.3457 9 (IMG) −12.4205

The refractive index Nd2=1.726350 of the second lens G2 is set smallerthan the refractive index Nd1=2.001100 of the first lens G1, and acemented surface between the exit surface of the first lens G1 and theincident surface of the second lens G2 is formed as a lens surfacehaving a convex shape facing the object side so as to have negativepower.

The refractive index Nd3=1.670939 of the third lens G3 is set smallerthan the refractive index Nd1=1.726350 of the second lens G2, and acemented surface between the exit surface of the second lens G2 and theincident surface of the third lens G3 is formed as a lens surface havinga convex shape facing the object side so as to have negative power. Theexit surface of the third lens G3 is formed as a lens surface having aconvex shape facing the object side so as to have negative power.

The refractive index Nd5=2.000800 of the fifth lens G5 is set largerthan the refractive index Nd4=1.882997 of the fourth lens G4, and thecemented surface between the exit surface of the fourth lens G4 and theincident surface of the fifth lens G5 is formed as a lens surface havinga convex shape facing the image side so as to have negative power.

In the imaging apparatus of this example, by these four lens surfaceshaving negative power, spherical aberration, axial chromatic aberration,chromatic spherical aberration, and the like generated on the incidentsurface of the first lens G1, the incident surface of the fourth lensG4, and the exit surface of the fifth lens G5 are appropriatelycorrected.

In addition, Table 10 shows specifications of the imaging apparatus ofthis example.

TABLE 10 Focal length of f_sys 11.997 (mm) imaging optical system Fvalue F/# 1.6 Angle of field 2ω 65.5 (deg) Entire length L_sys 17.959(mm) Distance from exit d_pup 14.060 (mm) pupil to image plane

The imaging apparatus of this example is an example of the imagingoptical system in which the aperture stop is disposed in the air layer,and the variable aperture stop is adopted. The bright optical systemhaving F/1.6 is realized by the simple structure having five lenses. Inaddition, the entire length is 17.959 (mm) with respect to a focallength of 11.997 (mm), and hence the optical system is compact, in whichL_sys/f_sys=1.50.

Table 11 shows values of Expressions (1), (2), and (4) in the imagingapparatus of this example.

TABLE 11 Conditional f_sys/d_pup 0.85 expression (1) Conditional|R_img|/f_sys 1.04 expression (2) Conditional |R_img|/d_pup 0.88expression (4)

The value of Expression (1) is 0.85, which satisfies the range ofExpression (1).

The value of Expression (2) is 1.04, which satisfies the range ofExpression (2).

Thus, field curvature, astigmatism, and lateral chromatic aberration canbe appropriately corrected over an angle of field of 65.5 (degrees).

The value of Expression (4) is 0.88, which satisfies the range ofExpression (4).

Thus, good optical performance can be obtained over a wide angle offield.

Table 12 shows values of power φ_fro of the optical system closer to theobject side than the aperture stop STO and power φ_beh of the opticalsystem closer to the image side than the aperture stop STO, Expression(3), and a power ratio φ_beh/φ_fro in the imaging apparatus of thisexample.

TABLE 12 Power of optical system closer φ_fro 0.0436 (1/mm) to objectside than aperture stop Power of optical system closer φ_beh 0.0839(1/mm) to image side than aperture stop Conditional 0 < φ_fro < φ_behSatisfied expression (3) Power ratio φ_beh/φ_fro 1.92

The power φ_fro of the optical system closer to the object side than theaperture stop STO is set different from the power φ_beh of the opticalsystem closer to the image side than the aperture stop STO. Thus,compared with a conventional ball lens, flexibility of aberrationcorrection is high, and ability of correcting spherical aberration oraxial chromatic aberration is improved.

FIG. 8 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 9 illustrates a lateral aberrationdiagram thereof.

In particular, the power φ_fro of the optical system closer to theobject side than the aperture stop STO is set smaller than the powerφ_beh of the optical system closer to the image side than the aperturestop STO, and hence spherical aberration can be appropriately corrected.

Specifically, as shown in Table 12, the imaging apparatus of thisexample is structured to satisfy Expression (10).φ_beh/φ_fro≧1.10  (10)

In other words, both the optical system closer to the object side thanthe aperture stop STO and the optical system closer to the image sidethan the aperture stop STO have positive power, and the power of theoptical system closer to the image side than the aperture stop STO isset approximately 20% larger than the power of the optical system closerto the object side than the aperture stop. Therefore, the ability ofcorrecting spherical aberration or axial chromatic aberration isimproved. Even the optical system in which the aperture stop is disposedin the air layer can obtain high imaging performance with a small Fvalue of F/1.6.

Example 4

An imaging optical system used for an imaging apparatus of this exampleincludes the aperture stop STO, six lenses G1 to G6, and a wave frontcontrol unit WFC as illustrated in FIG. 10.

The imaging optical system includes, in order from the object side: thefirst lens G1 that is a meniscus lens having a convex surface facing theobject side; the second lens G2 that is a meniscus lens having a convexsurface facing the object side; the third lens G3 that is a plano-convexlens having a convex surface facing the object side; the wave frontcontrol element WFC in which a phase difference is given to a cementedsurface between two flat glass plates; the aperture stop STO disposed onthe cemented surface between the two flat glass plates of the wave frontcontrol element WFC; the fourth lens G4 that is a plano-convex lenshaving a convex surface facing the image side; the fifth lens G5 that isa meniscus lens having a convex surface facing the image side; and thesixth lens G6 that is a meniscus lens having a convex surface facing theimage side.

All the optical elements from the first lens G1 to the sixth lens G6 arecemented to each other.

In this example, the same imaging unit ICU as that in Example 2 is used.

Tables 13A to 13D show a structure of the imaging apparatus of thisexample.

Surface number 1 is the incident surface of the first lens G1, surfacenumber 2 is the cemented surface between the exit surface of the firstlens G1 and the incident surface of the second lens G2, and surfacenumber 3 is the cemented surface between the exit surface of the secondlens G2 and the incident surface of the third lens G3.

In addition, surface number 4 is the cemented surface between the exitsurface of the third lens G3 and an incident surface of the wave frontcontrol element WFC, and surface number 5 is the cemented surfacebetween the two flat glass plates of the wave front control element WFC.At the position of surface number 5, a phase plate is disposed in aneffective part, and the aperture stop surface STO is disposed in anon-effective part.

Surface number 6 is a cemented surface between an exit surface of thewave front control element WFC and the incident surface of the fourthlens G4, surface number 7 is the cemented surface between the exitsurface of the fourth lens G4 and the incident surface of the fifth lensG5, and surface number 8 is a cemented surface between the exit surfaceof the fifth lens G5 and an incident surface of the sixth lens G6.

Surface number 9 is an exit surface of the sixth lens G6, and surfacenumber 10 is the image plane IMG, which is an incident surface of theoptical transmission unit OTM of the imaging unit ICU.

Further, the exit surface of the optical transmission unit OTM isconnected to the image sensor ICD.

In Table 13A, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number. Note that, the lens surface with a mark “(a)”in the R field is an aspherical surface while the lens surface with amark “(p)” is the phase difference plate.

As the aspherical shape in this example, a rotation symmetry asphericalsurface expressed by Expression (11) is used.

$\begin{matrix}{z = {\frac{{cr}^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}} + {Ar}^{4} + {Br}^{6} + {Cr}^{8} + {Dr}^{10}}} & (11)\end{matrix}$

Here, z represents a sag amount (mm) of the aspherical shape in theoptical axis direction, c represents a curvature (1/mm) on the opticalaxis, and r represents a distance (mm) from the optical axis in theradial direction. A, B, C, and D respectively represent coefficients offourth, sixth, eighth, and tenth orders.

In addition, the phase difference given to the phase difference plate inthis example is expressed by a rotation symmetry phase polynomial andhas a phase difference distribution expressed by Expression (12).

$\begin{matrix}{\phi = {\frac{{cr}^{2}}{1 + \sqrt{1 - {c^{2}r^{2}}}} + {C_{1}r^{2}} + {C_{2}r^{4}} + {C_{3}r^{6}} + {C_{4}r^{8}}}} & (12)\end{matrix}$

Here, φ represents a phase difference (wavelength), and C₁, C₂, C₃, andC₄ represent coefficients of second, fourth, sixth, and eighth orders,respectively. These are shown in the following Tables 13A to 13D.

TABLE 13A Surface number R D Nd νd  1 9.2576(a) 1.0868 1.922860 18.9  24.2724 4.5322 1.849860 24.1  3 20.4855 1.5758 1.922860 20.9  4 (WFC)Infinity 0.2500 1.516800 64.2  5 (STO) Infinity(p) 0.2500 1.516800 64.2 6 Infinity 1.0208 1.882023 37.2  7 −8.1725 2.6185 1.756999 47.7  8−3.6502 1.9300 1.804855 24.7  9 −7.9006(a) 2.3903 10 (IMG) −9.57691.0868

TABLE 13B Aspherical surface coefficients (Surface number 1) ParameterSymbol Value Conic constant K −2.45628E+00 Fourth order coefficient A3.21177E−04 Sixth order coefficient B −1.74680E−06 Eighth ordercoefficient C 0.00000E+00 Tenth order coefficient D 0.00000E+00

TABLE 13C Aspherical surface coefficients (Surface number 9) ParameterSymbol Value Conic constant K −1.21591E+01 Fourth order coefficient A−2.59045E−03 Sixth order coefficient B 1.30885E−04 Eighth ordercoefficient C −4.66439E−06 Tenth order coefficient D 7.14736E−08

TABLE 13D Phase difference polynomial (Surface number 5) ParameterSymbol Value Diffraction order First order Normalized wavelength587.5618 (nm) Second order coefficient C₁ −8.67933E−03 Fourth ordercoefficient C₂ 4.41119E−04 Sixth order coefficient C₃ 0.00000E+00 Eighthorder coefficient C₄ 0.00000E+00

In the imaging apparatus of this example, the incident surface of thefirst lens G1 as a lens closest to the object side and the exit surfaceof the fifth lens G5 as a lens closest to the image side are asphericalsurfaces, which have an aspherical shape having power weakening in theperiphery. Thus, spherical aberration is corrected.

In addition, Table 14 shows the specifications of the imaging apparatusof this example.

TABLE 14 Focal length of f_sys 7.499 (mm) imaging optical system F valueF/# 1.0 Angle of field 2ω 74.0 (deg) Entire length L_sys 13.264 (mm)Distance from exit d_pup 7.166 (mm) pupil to image plane

The imaging apparatus of this example improves the ability of correctingspherical aberration by setting the incident surface of the lens closestto the object side and the exit surface of the lens closest to the imageside to be aspherical surfaces and by disposing the wave front controlelement at the position of the aperture stop. Even in the case of a longfocal length of 7.499 (mm), it is possible to realize good imagingperformance in a bright optical system of F/1.0.

Table 15 shows values of Expressions (1), (2), and (4) in the imagingapparatus of this example.

TABLE 15 Conditional f_sys/d_pup 1.05 expression (1) Conditional|R_img|/f_sys 1.28 expression (2) Conditional |R_img|/d_pup 1.34expression (4)

The value of Expression (1) is 1.05 and satisfies Expression (1).

The value of Expression (2) is 1.28 and satisfies the range ofExpression (2).

The value of Expression (4) is 1.34 and satisfies the range ofExpression (4).

Thus, field curvature, astigmatism, and lateral chromatic aberration canbe easily corrected over an angle of field of 74.0 (degrees), and hencethe bright optical system of F/1.0 is realized.

FIG. 11 illustrates an axial aberration diagram in the imaging opticalsystem of this example, and FIG. 12 illustrates a lateral aberrationdiagram thereof.

Table 16 shows values of power φ_fro of the optical system closer to theobject side than the aperture stop STO and power φ_beh of the opticalsystem closer to the image side than the aperture stop STO, and a powerratio φ_beh/φ_fro in the imaging apparatus of this example.

TABLE 16 Power of optical system closer to φ_fro 0.0862 (1/mm) objectside than aperture stop Power of optical system closer to φ_beh 0.1018(1/mm) image side than aperture stop Conditional 0 < φ_fro < φ_behSatisfied expression (3) Power ratio φ_beh/φ_fro 1.18

The power φ_fro of the optical system closer to the object side than theaperture stop STO is set different from the power φ_beh of the opticalsystem closer to the image side than the aperture stop STO. Thus,compared with a conventional ball lens, flexibility of aberrationcorrection is high, and ability of correcting spherical aberration oraxial chromatic aberration is improved.

In particular, the power φ_fro of the optical system closer to theobject side than the aperture stop STO is set smaller than the powerφ_beh of the optical system closer to the image side than the aperturestop STO, and hence spherical aberration can be appropriately corrected.

Specifically, as shown in Table 16, the imaging apparatus of thisexample is structured to satisfy Expression (3).

Further, the structure satisfies Expression (7) described in Example 2,and the effect of this embodiment is sufficiently obtained.

In other words, both the optical system closer to the object side thanthe aperture stop STO and the optical system closer to the image sidethan the aperture stop STO have positive power, and the power of theoptical system closer to the image side than the aperture stop STO isset approximately 20% larger than the power of the optical system closerto the object side than the aperture stop. Therefore, the ability ofcorrecting spherical aberration or axial chromatic aberration isimproved. Even the optical system in which the aperture stop is disposedin the air layer can obtain high imaging performance with a small Fvalue of F/1.0.

(Second Embodiment)

This embodiment has a structure in which the wave front control elementis disposed close to the aperture stop of the imaging optical system soas to improve the effect of correcting axial aberration.

Next, the structure of the above-mentioned wave front control elementdisposed close to the aperture stop is described more in detail.

The wave front control element can correct aberration by giving a phasedifference to a wave front of the light beam and is, for example, aphase control element such as a phase difference plate, a diffractiveoptical element, and a phase modulation type spatial light modulator(liquid crystal element), or an aspherical surface having a very smallaspherical amount.

In this embodiment, the wave front control element is disposed close tothe aperture stop (including on the aperture stop) so as to give a phasedifference to the light beam passing through the aperture stop. Thus,aberration can be appropriately corrected.

When the wave front control element is disposed close to the aperturestop, the influence of the wave front control element on off-axialaberration can be minimized. Therefore, the phase differencedistribution of the wave front control element can have an optimal shapefor correcting axial aberration, and the effect of correcting axialaberration can be improved.

Here, when a phase difference distribution, in which a phase of the wavefront is delayed along with being away from the optical axis, is givento a phase of the wave front on the optical axis, spherical aberrationcan be appropriately corrected.

Note that, in this specification, the phrase “close to the aperturestop” is defined as between the lens closest to the aperture stop on theobject plane side of the aperture stop and the lens closest to theaperture stop on the image plane side of the aperture stop.

In addition, because the imaging optical system is close to a pointsymmetry optical system, the same aberration remains in the axial lightand in each off-axis light beam, and the aberration can be appropriatelycorrected by the common phase difference distribution shape.

In other words, when the wave front control element is disposed close tothe aperture stop surface of the imaging optical system that is close toa point symmetry optical system, aberration can be appropriatelycorrected in a wide angle of field even in a bright optical systemhaving an F value smaller than F/2.0. Further, the same effect can beobtained even in a very bright optical system having an F value smallerthan F/1.4.

In addition, because the imaging optical system having a small F valuehas a narrow depth of field, even the compact camera can take an imagein which background other than the focused plane is blurred.

Further, because the imaging optical system having a small F value canset the exposure time short in proportion to the square of the F value,blur due to shaking or image blur due to movement of an object, and shotnoise can be greatly reduced. Thus, it is possible to provide an imagingapparatus that can take high quality images.

In the following, specific examples of this embodiment are described.

Example 5

An imaging optical system used for an imaging apparatus of this exampleincludes three lenses G1, G2, and G3, and a wave front control unit WCMthat also works as the aperture stop STO as illustrated in FIG. 15.

The imaging optical system includes, in order from the object side, thefirst lens G1 as a plano-convex lens having a convex surface facing theobject side, the wave front control unit WCM, the second lens G2 as aplano-convex lens having a convex surface facing the image side, and thethird lens G3 as a meniscus lens having a convex surface facing theimage side. The exit surface of the first lens G1 is cemented to anincident surface of the wave front control unit WCM, an exit surface ofthe wave front control unit WCM is cemented to the incident surface ofthe second lens G2, and the exit surface of the second lens G2 iscemented to the incident surface of the third lens G3.

FIG. 16 is a schematic diagram of the wave front control unit WCM of theimaging apparatus of this example.

The wave front control unit WCM of the imaging apparatus of this exampleis constituted by two flat plates cemented to each other. In theeffective part of the cemented surface, there are formed binarydiffraction gratings BDG_a and BDG_b as a wave front control element WCDthat gives a phase difference, so as to mainly correct sphericalaberration and chromatic spherical aberration.

In addition, the wave front control unit WCM includes the light blockingmember disposed in the non-effective part of the cemented surfacebetween the two flat plates, which constitutes the aperture stop STO.

Note that, the wave front control element WCD is disposed on theaperture stop STO in this example. However, as illustrated in FIGS. 17to 20, the wave front control element WCD may be disposed at anyposition between the lens closest to the aperture stop on the objectplane side of the aperture stop and the lens closest to the aperturestop on the image plane side of the aperture stop.

The binary diffraction gratings BDG_a and BDG_b have the referencewavelength of the d-line, and the phase difference changes along withbeing away from the optical axis. Every time when the phase differenceexceeds an integral multiple of the reference wavelength, a stepdifference of the binary diffraction grating is increased by one step.

The wave front control element WCD of this example has a structure inwhich the phase difference increases along with being away from theoptical axis. The refractive index of the binary diffraction gratingBDG_a is set higher than the refractive index of the binary diffractiongrating BDG_b, and hence a desired phase difference is given to the wavefront passing through the wave front control element WCD.

Note that, the binary diffraction grating BDG_b is not limited to airbut may be optical glass or optical plastic. By setting the refractiveindex of the binary diffraction grating BDG_a higher than the refractiveindex of the binary diffraction grating BDG_b, it is possible to reducetotal reflection of a wide angle of field light beam at an interface ofthe diffraction grating.

In FIG. 15, IMG represents an image plane.

As illustrated in FIG. 15, the image plane IMG of the imaging apparatusin this example is an incident surface of the optical transmission unitOTM that is formed into a spherical shape, which is formed along thefield curvature of the imaging optical system. Therefore, good imageformation is realized over the entire region of the image plane IMG.

The optical transmission unit OTM of the imaging apparatus in thisexample is an image fiber formed of bound optical fibers of a few micronpitch and has a role of transmitting an image formed on the image planeof the imaging optical system to the image sensor ICD.

The exit surface of the optical transmission unit OTM is formed to be aflat surface and is held in close contact with the image sensor ICD forconnection, and thus the imaging unit ICU is formed.

The optical transmission unit OTM is used in this example. However,compared with a structure in which the image sensor itself is formedinto a spherical surface shape, there is the advantage of easyproduction of the imaging unit ICU in which one surface of the opticaltransmission unit OTM is formed into a spherical surface shape while theother surface is connected to the image sensor ICD.

Table 17 shows a structure of the imaging apparatus of this example.

Surface number 1 is the incident surface of the first lens G1, surfacenumber 2 is a cemented surface between the exit surface of the firstlens G1 and the incident surface of the wave front control unit WCM, andsurface number 3 is a cemented surface between the two flat glass platesof the wave front control unit WCM. The wave front control element WCDis disposed in the effective part, and the aperture stop STO is disposedin the non-effective part.

In this way, in the imaging apparatus of this example, the wave frontcontrol element WCD is disposed in the surface of the aperture stop STO.

Surface number 4 is the cemented surface between the exit surface of thewave front control unit WCM and the incident surface of the second lensG2, surface number 5 is the cemented surface between the exit surface ofthe second lens G2 and the incident surface of the third lens G3, andsurface number 6 is the exit surface of the third lens G3.

Surface number 7 is the image plane IMG, which is the incident surfaceof the optical transmission unit OTM. Further, the exit surface of theoptical transmission unit OTM (not shown) is connected to the imagesensor ICD.

In Table 17, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number. Note that, the surface with a mark “(p)” isthe wave front control element.

TABLE 17 Configuration table Surface number R D Nd νd 1 5.6187 4.5201.74400 44.8 2 Flat 0.263 1.51680 64.2 surface 3 (STO) Flat 0.2631.51680 64.2 surface(p) 4 Flat 1.990 1.83481 42.7 surface 5 −2.32182.938 2.00170 20.6 6 −6.3973 2.148 7 (IMG) −7.3276 4.520

The phase distribution shape given to the wave front control element WCDin the imaging apparatus of this example has a rotation symmetry shapewith respect to the optical axis and is expressed by the phasepolynomial of Expression (13).φ(r)=C ₁ r ² +C ₂ r ⁴ +C ₃ r ⁶ +C ₄ r ⁸ +C ₅ r ¹⁰+ . . .   (13)

Here, r represents a distance (mm) from the optical axis, φ(r)represents a phase difference (wavelength) at each distance r from theoptical axis, and C₁, C₂, C₃, C₄ and C₅ represent coefficients ofsecond, fourth, sixth, eighth, and tenth orders, respectively.

Table 18 shows parameters of the phase polynomial of the wave frontcontrol element WCD of surface number 3.

TABLE 18 Phase polynomial (Surface number 3) Parameter Symbol ValueDiffraction order First order Normalized wavelength 587.5618 (nm) Secondorder coefficient C₁ 0.00000E+00 Fourth order coefficient C₂ 5.18443E−04Sixth order coefficient C₃ 0.00000E+00 Eighth order coefficient C₄0.00000E+00 Tenth order coefficient C₅ 0.00000E+00

The wave front control element WCD of the imaging apparatus of thisexample uses only the fourth order term of the phase polynomial ofExpression (13).

FIG. 21 shows the phase difference distribution given to the wave frontcontrol element WCD of this example.

In the wave front control element WCD, the phase difference is increasedin a positive direction along with being away from the optical axis, soas to form a wave front in which the phase is gradually delayed alongwith being away from the optical axis.

Power P(r) due to the phase difference of the wave front control elementWCD is determined by calculating a second order differential of thephase polynomial of Expression (13) by the distance r from the opticalaxis and by multiplying the result by “−1”, which is expressed byExpression (14).P(r)=−(2C ₁+12C ₂ r ²+30C ₃ r ⁴+56C ₄ r ⁶+90C ₅ r ⁸+ . . . )  (14)

Further, because power P(0) due to the phase difference on the opticalaxis (r=0) is −2C₁, a difference between the power P(r) due to the phasedifference at each distance r and the power P(0) due to the phasedifference on the optical axis (r=0), namely, a power difference ΔP(r)due to the phase difference is expressed by Expression (15).ΔP(r)=−(12C ₂ r ²+30C ₃ r ⁴+56C ₄ r ⁶+90C ₅ r ⁸+ . . . )  (15)

FIG. 22 shows the power difference ΔP(r) due to the phase difference ofthe wave front control element WCD of this example.

The wave front control element WCD has power gradually increasing in anegative direction along with being away from the optical axis and hasthe effect of moving a condensed position of the light beam having ahigh incident height position backward. The imaging optical system haspositive power as a whole, and the spherical aberration tends to be“under”. Therefore, the light ray having a higher incident heightposition forms the image further frontward than the light ray close tothe optical axis.

Therefore, based on the effect of the wave front control element WCD ofthis example, the condensed position at a higher incident heightposition is moved further backward. Thus, spherical aberration can becorrected.

This tendency is more conspicuous in the imaging optical system having asmaller F value, and hence the effect of correcting spherical aberrationby the wave front control element WCD becomes larger.

As to chromatic spherical aberration, an amount or a shape of sphericalaberration of the C-line (656.2725 nm), the F-line (486.1327 nm), or theg-line (435.8343 nm), for example, is different from that of thereference wavelength d-line (587.5618 nm), and hence there is a problemin that the condensed position cannot be on the same image plane.Specifically, with respect to the reference wavelength d-line, there isa tendency that an amount of being “under” of spherical aberrationincreases at a high incident height position in a short wavelength suchas the F-line or the g-line, while the amount of being “under” ofspherical aberration decreases at a high incident height position in along wavelength such as the C-line.

As to the power due to the phase difference, stronger power can beobtained for a shorter wavelength. Therefore, also in the wave frontcontrol element WCD of this example, a correction amount of sphericalaberration becomes larger for a shorter wavelength so that chromaticspherical aberration can be corrected.

FIG. 23 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 24 illustrates a lateral aberrationdiagram thereof. As illustrated in FIG. 23, spherical aberration, axialchromatic aberration, astigmatism, field curvature, distortion, andchromatic spherical aberration are appropriately corrected.

Here, the chromatic spherical aberration is defined as a differencebetween the spherical aberration amount of the reference wavelength (forexample, d-line) and the spherical aberration amount of each wavelength(for example, C-line, F-line, or g-line).

In particular, the light beam in the entire region from a low incidentlight beam height to a high incident light beam height can be condensedon the image plane, and hence spherical aberration can be veryappropriately corrected.

In addition, axial chromatic aberration and chromatic sphericalaberration are also very appropriately corrected so that high imagingperformance is obtained.

As illustrated in FIG. 24, good performance is obtained in each fieldangle light beam, and coma, field curvature, and lateral chromaticaberration are appropriately corrected.

Table 19 shows the specifications of the imaging apparatus of thisexample.

TABLE 19 Focal length of imaging f_sys 6.699 (mm) optical system F valueF/# 1.40 Angle of field 2ω 90.0 (deg) Entire length L_sys 9.974 (mm)Distance from exit pupil d_pup 6.595 (mm) to image plane Distance fromaperture d_ape 7.340 (mm) stop to image plane Distance from apertured_ape_last 5.191 (mm) stop to last plane

The imaging apparatus of this example has a small F value of F/1.4, awide angle of field of 90.0 (degrees), and a compact size with theentire length of 9.974 (mm), which is an example of the imagingapparatus in which brightness, high resolution, a very wide angle offield, and a compact size are realized at the same time.

Table 20 shows values of Expressions (1), (2), (4), and (17) of theimaging apparatus of this example.

TABLE 20 Conditional expression (1) f_sys/d_pup 1.02 Conditionalexpression (2) |R_img|/f_sys 1.09 Conditional expression (4)|R_img|/d_pup 1.11 Conditional expression (17) d_pup/d_ape 0.899

The value of Expression (1) is 1.02 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemon the image side of the aperture stop can be close to a point symmetrystructure, and hence coma, astigmatism, distortion, and lateralchromatic aberration can be appropriately corrected.

The value of Expression (2) is 1.09 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a wide angle of field of 90.0 (degrees).

When Expressions (1) and (2) are satisfied, focus adjustment can beperformed from infinity to a close distance only by changing thedistance between the imaging optical system and the image plane withoutchanging the image plane shape.

In addition, in the imaging apparatus of this embodiment, a radius ofcurvature of the image plane is set substantially equal to the distancefrom the exit pupil to the image plane of the imaging optical system.

The value of Expression (4) is 1.11 and satisfies the range ofExpression (4).

Thus, the imaging optical system is close to a point symmetry structure,and hence coma, astigmatism, distortion, and lateral chromaticaberration are appropriately corrected. Further, focus adjustment can beperformed while maintaining high resolution in a wide focus adjustmentrange from infinity to a close distance.

In the imaging apparatus of this example, the wave front control elementWCD is disposed on the surface of the aperture stop STO, and coma occursdue to a phase difference given to the wave front control element WCD.

The wave front control element WCD of this example delays the wave frontof the light beam at the periphery with respect to the optical axis.

Because the field angle light beam obliquely enters the wave frontcontrol element WCD, the distance from the wave front control elementWCD to the image plane is different between the upper ray and the lowerray. As a result, a large optical path difference occurs and causescoma.

This is described with reference to FIG. 15. The distance from the wavefront control element WCD to the plane closest to the image side islonger for the upper ray than for the lower ray of the field angle lightbeam.

In other words, on the plane closest to the image side, the lower rayreaches a position further apart from the principal ray than the upperray.

Therefore, it is necessary to set a distance from a reach point of eachlight ray on the lens surface closest to the image side to an imagepoint on the image plane to be longer for the lower ray than for theupper ray.

In the imaging apparatus of this embodiment, the image plane has aconcentric shape for the field angle light beam. Therefore, in a usualcase, the distance from a reach point of each light beam on the lenssurface closest to the image side to an image point on the image planeis almost the same between the upper ray and the lower ray.

However, in the imaging apparatus of this example, the field angle lightbeam propagates from the lens surface closest to the image side to theimage plane so as to expand outward. Thus, the distance from a reachpoint of each light ray on the lens surface closest to the image side toan image point on the image plane is longer for the lower ray than forthe upper ray.

In this way, coma can be appropriately corrected.

Specifically, it is preferred to dispose the curvature center from thelens surface closest to the image side to be closer to the object sidethan the aperture stop.

In the imaging apparatus of this example, the radius of curvature of thelens surface closest to the image side is R_last=−6.3973 (mm), and thedistance from the aperture stop to the lens surface closest to the imageside is d_ape_last=5.191 (mm).

Therefore, the relationship of Expression (16) is satisfied, and thecurvature center from the lens surface closest to the image side isdisposed closer to the object side than the aperture stop.|R_last|>d_ape_last  (16)

In addition, the distance from the exit pupil to the image plane of theimaging optical system d_pup=6.595 (mm) is set shorter than the distancefrom the aperture stop to the image plane d_ape=7.340 (mm), and hencethe field angle light beam expands outward when propagating from thelens surface closest to the image side to the image plane.

In this case, when the condition of Expression (8) is satisfied, comacan be appropriately corrected.0.7≦d_pup/d_ape≦0.95  (17)

Next, an action of improving the peripheral darkening is described.

In the imaging optical system of the imaging apparatus of this example,the radius of curvature of the image plane is set substantially equal tothe focal length of the imaging optical system. Thus, the focal lengthcan be substantially uniform in the full angle of field.

Thus, the square of cos ω of the peripheral light intensity ratio can beimproved.

The largest half angle of field in this example is ω=45.0 (degrees) sothat cos² ω is 0.5 in contrast to cos⁴ ω=0.25. Thus, peripheral lightintensity can be improved by 2 times.

By satisfying Expression (2), it is possible to obtain a reasonableeffect.

Further, in the imaging optical system of the imaging apparatus of thisexample, the radius of curvature of the image plane is set substantiallyequal to the distance from the exit pupil to the image plane of theimaging optical system, and hence the incident angle to the image planecan be substantially orthogonal.

Thus, the peripheral light intensity ratio can be improved by the firstpower of cos ω.

The largest half angle of field in this example is ω=45.0 (degrees) sothat cos³ ω is 0.35 in contrast to cos⁴ ω=0.25. Thus, peripheral lightintensity can be improved by 1.4 times.

By satisfying Expression (4), it is possible to obtain a reasonableeffect.

By satisfying Expressions (2) and (4) at the same time, the peripherallight intensity ratio can be improved by the third power of cos ω, andhence the peripheral light intensity can be improved by 2.8 times.

Thus, because the peripheral light intensity ratio of the imagingoptical system having a wide angle of field can be significantlyimproved, it is possible to provide the imaging apparatus that can takean image having high image quality with high contrast and little noiseover a wide angle of field.

As described above, according to the structure of this example, it ispossible to realize the imaging apparatus having good imagingperformance over a wide angle of field even at an F value smaller thanF/2.0 with a compact structure.

In addition, the peripheral darkening can be significantly improved, andhence it is possible to realize the imaging optical system that is verybright over a wide angle of field.

Thus, because the exposure time can be significantly reduced, it ispossible to provide the imaging apparatus that can take an image havinghigh quality with appropriately reduced blur due to shaking, image blurdue to movement of the object, and noise.

In addition, it is possible to provide the imaging optical system withthe compact structure in which a defocused subject can be significantlyblurred.

Further, using the above-mentioned high performance imaging opticalsystem with the simple structure, focus adjustment can be performed in awide range from infinity to a close distance with little deteriorationof imaging performance.

Example 6

An imaging optical system used for an imaging apparatus of this exampleincludes four lenses G1, G2, G3, and G4, the aperture stop STO, and awave front control element WCD as illustrated in FIG. 25.

The imaging optical system includes, in order from the object side: afirst lens G1 as a meniscus lens having a convex surface facing theobject side; a second lens G2 as a plano-convex lens having a convexsurface facing the object side; a third lens G3 as a plano-convex lenshaving a convex surface facing the image side; and a fourth lens G4 as ameniscus lens having a convex surface facing the image side.

In FIG. 25, IMG represents an image plane. As illustrated in FIG. 25,the image plane IMG of the imaging apparatus in this example is anincident surface of the optical transmission unit OTM that is formedinto a spherical shape, which is formed along the field curvature of theimaging optical system. Therefore, good image formation is realized overthe entire region of the image plane IMG.

The optical transmission unit OTM of the imaging apparatus in thisexample is an image fiber formed of bound optical fibers of a few micronpitch and has a role of transmitting an image formed on the image planeof the imaging optical system to the image sensor ICD.

The exit surface of the optical transmission unit OTM is formed to be aflat surface and is held in close contact with the image sensor ICD forconnection, and thus the imaging unit ICU is formed.

Table 21 shows a structure of the imaging apparatus of this example.

Surface number 1 is the incident surface of the first lens G1 and has arotation symmetry aspherical shape expressed by the polynomial ofExpression (11).

Surface number 2 is the cemented surface between the exit surface of thefirst lens G1 and the incident surface of the second lens G2, andsurface number 3 is the cemented surface between the exit surface of thesecond lens G2 and the incident surface of the third lens G3. The wavefront control element WCD is disposed in the effective part, and theaperture stop STO is disposed in the non-effective part.

In this way, in the imaging apparatus of this example, the wave frontcontrol element WCD is disposed on the surface of the aperture stop STO.

Surface number 4 is the cemented surface between the exit surface of thethird lens G3 and the incident surface of the fourth lens G4, andsurface number 5 is the exit surface of the fourth lens G4, which has arotation symmetry aspherical shape expressed by the polynomial ofExpression (11).

Surface number 7 is the image plane IMG, which is the incident surfaceof the optical transmission unit OTM. Further, the exit surface of theoptical transmission unit OTM (not shown) is connected to the imagesensor ICD.

In Table 21, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number. Note that, the surface with a mark “(a)” isan aspherical surface while the surface with a mark “(p)” is a surfaceprovided with the wave front control element in the effective part.

TABLE 21 Configuration table Surface number R d Nd νd 1 9.0932(a) 2.76362.00060 25.5 2 3.3892 5.2692 2.00100 29.1 3 (STO) Flat 2.9521 1.9108235.3 surface(p) 4 −3.1249 2.9342 2.00270 19.3 5 −8.0232(a) 1.6787 6(IMG) −9.1592

The aspherical surface of the imaging apparatus of this example has arotation symmetry aspherical surface whose center is the optical axisand is expressed by the polynomial of Expression (11).

The aspherical surface coefficients of the first surface of the imagingapparatus of this example are shown in Table 22A, the aspherical surfacecoefficients of the fifth surface are shown in Table 22B, and thecoefficients of the phase difference polynomial of the third surface areshown in Table 22C.

TABLE 22A Aspherical surface coefficients (Surface number 1) ParameterSymbol Value Conic constant K −7.67865E−01 Fourth order coefficient A8.91147E−05 Sixth order coefficient B 8.34469E−07 Eighth ordercoefficient C −1.30692E−08 Tenth order coefficient D 1.51136E−10

TABLE 22B Aspherical surface coefficients (Surface number 5) ParameterSymbol Value Conic constant K −8.00433E+00 Fourth order coefficient A−1.68038E−03 Sixth order coefficient B 5.00405E−05 Eighth ordercoefficient C −1.02512E−06 Tenth order coefficient D 5.65476E−09

TABLE 22C Phase polynomial (Surface number 3) Parameter Symbol ValueDiffraction order First order Normalized wavelength 587.5618 (nm) Secondorder coefficient C₁ −5.72626E−03 Fourth order coefficient C₂5.73805E−04 Sixth order coefficient C₃ 4.34455E−06 Eighth ordercoefficient C₄ −1.44872E−06 Tenth order coefficient C₅ 7.68743E−09

As shown in Table 22C, the wave front control element WCD of thisexample uses the second to the tenth power terms of the phase polynomialof Expression (13) so as to give the phase difference.

FIG. 26 shows a phase difference distribution given to the wave frontcontrol element WCD of this example.

The wave front control element WCD increases the phase difference in thenegative direction along with being away from the optical axis, so as toform the wave front in which the phase is advanced gradually along withbeing away from the optical axis.

Positive power is given to the whole light beam, and the wave frontcontrol element WCD shares a part of power of the imaging opticalsystem.

On the other hand, the wave front control element WCD has a role ofcorrecting spherical aberration.

In order to correct spherical aberration, it is important to move acondensed position of the light beam at a high incident height positionwith respect to a condensed position of the axial light. As indicated byExpression (15), a power difference due to the phase difference betweena light ray at a high incident height position and the optical axis isimportant.

The imaging optical system has positive power as a whole, and thespherical aberration tends to be “under”. Therefore, the light rayhaving a higher incident height position forms the image furtherfrontward than the light ray close to the optical axis.

When power in a relatively negative direction is given to the former,the effect of moving the condensed position of the light ray at a highincident height position backward is obtained, and spherical aberrationcan be corrected.

FIG. 27 shows the power difference ΔP(r) due to the phase difference ofthe wave front control element WCD of this example. The wave frontcontrol element WCD has power gradually increasing in the negativedirection along with being away from the optical axis, and hencespherical aberration can be appropriately corrected.

In the imaging optical system having a very small F value equal to orsmaller than F/1.4, this tendency becomes more conspicuous as eachincident position is higher so that there is greater significance ofcorrecting spherical aberration by the wave front control element WCD.As to chromatic spherical aberration, an amount or a shape of sphericalaberration of the C-line (656.2725 nm), the F-line (486.1327 nm), or theg-line (435.8343 nm), for example, is different from that of thereference wavelength d-line (587.5618 nm), and hence there is a problemin that the condensed position cannot be on the same image plane.

Specifically, with respect to the reference wavelength d-line, there issuch a tendency that an amount of being “under” of spherical aberrationincreases at a high incident height position in a short wavelength suchas the F-line or the g-line, while the amount of being “under” ofspherical aberration decreases at a high incident height position in along wavelength such as the C-line.

As to the power due to the phase difference, stronger power can beobtained for a shorter wavelength. Therefore, also in the wave frontcontrol element WCD of this example, a correction amount of sphericalaberration becomes larger for a shorter wavelength so that chromaticspherical aberration can be corrected.

FIG. 28 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 29 illustrates a lateral aberrationdiagram thereof.

As illustrated in FIG. 28, spherical aberration, axial chromaticaberration, astigmatism, field curvature, distortion, and chromaticspherical aberration are appropriately corrected.

Here, the chromatic spherical aberration is defined as a differencebetween the spherical aberration amount of the reference wavelength (forexample, d-line) and the spherical aberration amount of each wavelength(for example, C-line, F-line, or g-line).

In particular, the light beam in the entire region from a low incidentlight beam height to a high incident light beam height can be condensedon the image plane, and hence spherical aberration can be veryappropriately corrected.

In addition, axial chromatic aberration and chromatic sphericalaberration are also very appropriately corrected so that high imagingperformance is obtained.

As illustrated in FIG. 29, good performance is obtained in each fieldangle light beam, and coma, field curvature, and lateral chromaticaberration are appropriately corrected.

Table 23 shows the specifications of the imaging apparatus of thisexample.

TABLE 23 Focal length of imaging f_sys 7.499 (mm) optical system F valueF/# 1.00 Angle of field 2ω 90.0 (deg) Entire length L_sys 13.919 (mm)Distance from exit pupil d_pup 6.334 (mm) to image plane Distance fromaperture d_ape 7.565 (mm) stop to image plane Distance from apertured_ape_last 5.886 (mm) stop to last plane

The imaging apparatus of this example has a small F value of F/1.0, awide angle of field of 90.0 (degrees), and a compact size with theentire length of 9.974 (mm), which is an example of the imagingapparatus in which brightness, high resolution, a very wide angle offield, and a compact size are realized at the same time.

Table 24 shows values of Expressions (1), (2), (4), and (17) of theimaging apparatus of this example.

TABLE 24 Conditional f_sys/d_pup 1.18 expression (1) Conditional|R_img|/f_sys 1.22 expression (2) Conditional |R_img|/d_pup 1.45expression (4) Conditional d_pup/d_ape 0.837 expression (17)

The value of Expression (1) is 1.18 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemin the image aide of the aperture stop can be close to a point symmetrystructure, and hence coma, astigmatism, distortion, and lateralchromatic aberration can be appropriately corrected.

The value of Expression (2) is 1.22 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a wide angle of field of 90.0 (degrees).

The value of Expression (4) is 1.45 and satisfies the range ofExpression (4). Thus, the imaging optical system is close to a pointsymmetry structure, and hence coma, astigmatism, distortion, and lateralchromatic aberration are appropriately corrected.

Further, in the imaging apparatus of this example, the distance betweenthe imaging optical system and the image plane is changed so as toperform focus adjustment. Because Expression (4) is satisfied, it ispossible to perform focus adjustment while maintaining high resolutionin a wide focus adjustment range from infinity to a close distance.

In the imaging apparatus of this example, the radius of curvature of thelens surface closest to the image side is R_last=−8.0232 (mm), and thedistance from the aperture stop to the lens surface closest to the imageside is d_ape_last=5.886 (mm).

The relationship of Expression (16) is satisfied, and the curvaturecenter from the lens surface closest to the image side is disposedcloser to the object side than the aperture stop. Thus, the structure issuitable for appropriately correcting coma generated by the wave frontcontrol element WCD.

In addition, the distance from the exit pupil to the image plane of theimaging optical system d_pup=6.334 (mm) is set shorter than the distancefrom the aperture stop to the image plane d_ape=7.565 (mm), and hencethe field angle light beam expands outward when traveling from the lenssurface closest to the image side to the image plane.

Expression (17) is satisfied, and the structure is suitable forappropriately correcting coma generated by the wave front controlelement WCD.

Example 7

An imaging optical system used for an imaging apparatus of this exampleincludes six lenses G1 to G6, the aperture stop STO, and the wave frontcontrol unit WCM as illustrated in FIG. 30.

The imaging optical system includes, in order from the object side, thefirst lens G1 as a meniscus lens having a convex surface facing theobject side, the second lens G2 as a meniscus lens having a convexsurface facing the object side, and the third lens G3 as a plano-convexlens having a convex surface facing the object side.

Next, there are disposed the wave front control unit WCM, the fourthlens G4 as a plano-convex lens having a convex surface facing the imageside, the fifth lens G5 as a meniscus lens having a convex surfacefacing the image side, and the sixth lens G6 as a meniscus lens having aconvex surface facing the image side.

All the optical elements from the first lens G1 to the sixth lens G6 arecemented to each other. In the imaging apparatus according to thisexample, the same imaging unit ICU as that in Example 5 is disposed.

Table 25 shows a structure of the imaging apparatus of this example.

Surface number 1 is the incident surface of the first lens G1, surfacenumber 2 is the cemented surface between the exit surface of the firstlens G1 and the incident surface of the second lens G2, and surfacenumber 3 is the cemented surface between the exit surface of the secondlens G2 and the incident surface of the third lens G3.

Surface number 4 is a cemented surface between the exit surface of thethird lens G3 and the incident surface of the wave front control unitWCM, and surface number 5 is the cemented surface between the two flatglass plates of the wave front control unit WCM. At the surface of thesurface number 5, the phase difference plate as the wave front controlelement WCD is disposed in the effective part, and the aperture stopsurface STO is disposed in the non-effective part.

Surface number 6 is a cemented surface between the exit surface of thewave front control unit WCM and the incident surface of the fourth lensG4, surface number 7 is the cemented surface between the exit surface ofthe fourth lens G4 and the incident surface of the fifth lens G5, andsurface number 8 is a cemented surface between the exit surface of thefifth lens G5 and the incident surface of the sixth lens G6.

In addition, surface number 9 is the exit surface of the sixth lens G6,and surface number 10 is the image plane IMG, which is the incidentsurface of the optical transmission unit OTM of the imaging unit ICU.

Further, the exit surface of the optical transmission unit OTM isconnected to the image sensor ICD.

In Table 25, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number. Note that, the lens surface with a mark “(a)”in the R field is an aspherical surface while the surface with a mark“(p)” is the wave front control element.

TABLE 25 Surface number R d Nd νd  1 9.2576(a) 1.0868 1.922860 18.9  24.2724 4.5322 1.849860 24.1  3 20.4855 1.5758 1.922860 20.9  4 Infinity0.2500 1.516800 64.2  5 (STO) Infinity(p) 0.2500 1.516800 64.2  6Infinity 1.0208 1.882023 37.2  7 −8.1725 2.6185 1.756999 47.7  8 −3.65021.9300 1.804855 24.7  9 −7.9006(a) 2.3903 10 (IMG) −9.5769 1.0868

The aspherical surface of the imaging apparatus of this example has arotation symmetry aspherical surface whose center is the optical axisand is expressed by the polynomial of Expression (11).

The aspherical surface coefficients of the first surface of the imagingapparatus of this example are shown in Table 26A, the aspherical surfacecoefficients of the ninth surface are shown in Table 26B, and thecoefficients of the phase difference polynomial of the fifth surface areshown in Table 26C.

TABLE 26A Aspherical surface coefficients (Surface number 1) ParameterSymbol Value Conic constant K −2.45628E+00 Fourth order coefficient A3.21177E−04 Sixth order coefficient B −1.74680E−06 Eighth ordercoefficient C 0.00000E+00 Tenth order coefficient D 0.00000E+00

TABLE 26B Aspherical surface coefficients (Surface number 9) ParameterSymbol Value Conic constant K −1.21591E+01 Fourth order coefficient A−2.59045E−03 Sixth order coefficient B 1.30885E−04 Eighth ordercoefficient C −4.66439E−06 Tenth order coefficient D 7.14736E−08

TABLE 26C Phase difference polynomial (Surface number 5) ParameterSymbol Value Diffraction order First order Normalized wavelength587.5618 (nm) Second order coefficient C₁ −8.67933E−03 Fourth ordercoefficient C₂ 4.41119E−04 Sixth order coefficient C₃ 0.00000E+00 Eighthorder coefficient C₄ 0.00000E+00 Tenth order coefficient C₅ 0.00000E+00

FIG. 31 shows the power difference ΔP(r) due to the phase difference ofthe wave front control element WCD of this example. The wave frontcontrol element WCD has a structure in which the power graduallyincreases in the negative direction along with being away from theoptical axis. Spherical aberration can be changed in the direction of“over”, and hence spherical aberration can be appropriately corrected.

In addition, as to the power due to the phase difference, the peripherypower is larger in the negative direction than the power on the opticalaxis so that spherical aberration can be changed further in thedirection of “over” for a short wavelength than for a long wavelength.Thus, chromatic spherical aberration can also be appropriatelycorrected.

FIG. 32 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 33 illustrates a lateral aberrationdiagram thereof.

As illustrated in FIG. 32, spherical aberration, axial chromaticaberration, astigmatism, field curvature, distortion, and chromaticspherical aberration are appropriately corrected.

In particular, the light beam in the entire region from a low incidentlight beam height to a high incident light beam height can be condensedon the image plane, and hence spherical aberration can be veryappropriately corrected.

In addition, axial chromatic aberration and chromatic sphericalaberration are also very appropriately corrected so that high imagingperformance is obtained.

As illustrated in FIG. 33, good performance is obtained in each fieldangle light beam, and coma, field curvature, and lateral chromaticaberration are appropriately corrected.

In the imaging apparatus of this example, the incident surface of thefirst lens G1 as the lens closest to the object side and the exitsurface of the fifth lens G5 as the lens closest to the image side areaspherical surfaces, which each have an aspherical shape in which thepower is reduced in the periphery, and hence spherical aberration iscorrected.

In addition, Table 27 shows the specifications of the imaging apparatusof this example.

TABLE 27 Focal length of imaging f_sys 7.499 (mm) optical system F valueF/# 1.0 Angle of field 2ω 74.0 (deg) Entire length L_sys 13.264 (mm)Distance from exit pupil to d_pup 7.166 (mm) image plane Distance fromaperture stop d_ape 8.210 (mm) to image plane Distance from aperturestop d_ape_last 5.819 (mm) to last plane

In the imaging apparatus of this example, the incident surface of thelens closest to the object side and the exit surface of the lens closestto the image side are aspherical surfaces. Further, the wave frontcontrol element is disposed at the position of the aperture stop, so asto improve ability of correcting spherical aberration. Thus, it ispossible to realize good imaging performance in the bright opticalsystem of F/1.0 even in the case of a long focal length of 7.499 (mm).

Table 28 shows values of Expressions (1), (2), (4), and (17) of theimaging apparatus of this example.

TABLE 28 Conditional expression (1) f_sys/d_pup 1.05 Conditionalexpression (2) |R_img|/f_sys 1.28 Conditional expression (4)|R_img|/d_pup 1.34 Conditional expression (17) d_pup/d_ape 0.873

The value of Expression (1) is 1.05 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemfrom the aperture stop to the image side can be close to a pointsymmetry structure, and hence coma, astigmatism, distortion, and lateralchromatic aberration can be appropriately corrected.

The value of Expression (2) is 1.28 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a wide angle of field.

The value of Expression (4) is 1.34 and satisfies the range ofExpression (4). Thus, the imaging optical system is close to a pointsymmetry structure, and hence coma, astigmatism, distortion, and lateralchromatic aberration are appropriately corrected. In addition, theimaging apparatus of the example also performs focus adjustment bychanging the distance between the imaging optical system and the imageplane. Because Expression (4) is satisfied, focus adjustment can beperformed in a wide focus adjustment range from infinity to a closedistance while maintaining high resolution.

In the imaging apparatus of this example, the radius of curvature of thelens surface closest to the image side is R_last=−7.9006 (mm), and thedistance from the aperture stop to the lens surface closest to the imageside is d_ape_last=5.819 (mm).

The relationship of Expression (16) is satisfied, and the curvaturecenter from the lens surface closest to the image side is disposedcloser to the object side than the aperture stop. Thus, the structure issuitable for appropriately correcting coma generated by the wave frontcontrol element WCD.

In addition, the distance from the exit pupil to the image plane of theimaging optical system d_pup=7.166 (mm) is set shorter than the distancefrom the aperture stop to the image plane d_ape=8.210 (mm). Thus, thefield angle light beam expands outward when propagating from the lenssurface closest to the image side to the image plane.

Expression (17) is satisfied, and hence the structure is suitable forappropriately correcting coma generated by the wave front controlelement WCD.

Thus, the very bright imaging apparatus of F/1.0 over an angle of fieldof 74.0 (degrees) is realized.

(Third Embodiment)

In this embodiment, an imaging optical system having a wide angle and asmall F value is structured to change an aperture stop diameter.

Next, the above-mentioned aperture stop is described in more detail.

The aperture stop of this embodiment has a feature that the aperturestop diameter can be variable.

In the ball lens described in Japanese Patent Application Laid-Open No.S63-081413, optical glass is filled in the opening of the aperture stopso that the aperture stop diameter cannot be changed.

Therefore, in this embodiment, the aperture stop is disposed in a fluidmedium so that the aperture stop diameter can be variable.

Here, the fluid medium means a gas such as air or a liquid such as wateror oil. In general, the fluid medium has a refractive index lower thanthat of an optical material such as optical glass or optical plastic.Therefore, a refractive index difference between the fluid medium andthe lens surface causes deterioration of optical performance.

For instance, a case of the ball lens in which a space around theaperture stop is filled with the fluid medium is described.

When the ball lens is divided into two at position of the aperture stopand the fluid medium is filled therebetween, the axial light is notaffected so much, but the field angle light beam is significantlyrefracted at the lens surface coming into contact with the fluid medium.

The ball lens corrects aberration by its point symmetry. However, if thefield angle light beam is significantly refracted at the interfacebetween the lens surface and the fluid medium, the point symmetry of theoptical path is significantly deteriorated so that large aberrationoccurs as a problem.

Specifically, due to the large refraction at the lens surface, coma,astigmatism, field curvature, or lateral chromatic aberrationsignificantly occurs and causes a problem.

In addition, when the region of the fluid medium is formed as aspherical surface whose center is the aperture stop, the point symmetryis maintained also for the field angle light beam.

However, because the distance to the aperture stop is short, the radiusof curvature of the spherical surface becomes small. As a result, therecauses a problem of light beam vignetting when a part of the field anglelight beam is totally reflected.

In other words, the imaging optical system having a small F value cannotbe realized.

Therefore, in this embodiment, the lens surface on the object side ofthe aperture stop, which comes into contact with the fluid medium, has ashape of a concave surface. Thus, refraction by the lens surface isreduced so as to suppress occurrence of aberration.

In addition, the lens surface on the image side of the aperture stop,which comes into contact with the fluid medium, has a shape of a convexsurface. Thus, the power given by the above-mentioned concave surface iscanceled. Thus, an angle of the field angle light beam in a rear unit isreset to an angle in a front unit, and the rear unit has a structureclose to a point symmetry optical system so that aberration can beappropriately corrected.

In this way, using the structure of this embodiment, it is possible toprovide the imaging apparatus that can change the aperture stop diameterin the imaging optical system having a wide angle and a small F value.In particular, a large effect can be obtained in a bright imagingoptical system having an F value smaller than F/2.0.

In the following, specific examples of this embodiment are described.

Example 8

An imaging optical system used for an imaging apparatus of this exampleincludes the four lenses G1, G2, G3, and G4 and the aperture stop STOdisposed in a fluid medium FM as illustrated in FIG. 34.

The imaging optical system includes, in order from the object side: thefirst lens G1 as a meniscus lens having a convex surface facing theobject side; the second lens G2 as a meniscus lens having a convexsurface facing the object side; the aperture stop STO; the third lens G3as a biconvex lens; and the fourth lens G4 as a meniscus lens having aconvex surface facing the image side.

In FIG. 34, IMG represents the image plane.

In the imaging apparatus according to this example, the image sensor ICDis formed into a sphere shape so as to form the curved image plane IMG.Thus, good imaging performance is realized over the entire region of theimage plane IMG.

Table 29 shows a structure of the imaging apparatus of this example.

Surface number 1 is the incident surface of the first lens G1, surfacenumber 2 is the cemented surface between the exit surface of the firstlens G1 and the second lens G2, surface number 3 is the exit surface ofthe second lens G2, and surface number 4 is the aperture stop STO.

Surface number 5 is the incident surface of the third lens G3, surfacenumber 6 is the cemented surface between the exit surface of the thirdlens G3 and the incident surface of the fourth lens G4, surface number 7is the exit surface of the fourth lens G4, and surface number 8 is theimage plane IMG.

In Table 29, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number.

TABLE 29 Configuration table Surface number R d Nd νd 1 2.3152 0.62871.79504 28.7 2 1.2804 0.9803 1.54814 45.9 3 15.6214 0.2500 Air 4 (STO)Flat 0.2500 Air surface 5 7.4031 1.8338 1.72000 46.0 6 −1.5547 0.75511.84681 23.6 7 −3.3021 1.4146 Air 8 (IMG) −3.6328

In the imaging apparatus of this example, the space between the secondlens G2 and the third lens G3 is filled with air as the fluid medium FM.The aperture stop STO is disposed in the air so that the aperture stopSTO has a variable aperture stop diameter.

In addition, the refractive index of the air is Nd=1.000, which issignificantly lower than that of the optical glass. Therefore, there isa problem in that the field angle light beam is refracted at theinterface between the optical glass and the air with a large angle,which causes large aberration.

In the imaging apparatus of this example, too, the refractive indexNd=1.000 of the air is significantly lower than the refractive indexNd₂=1.54814 of the second lens G2 and the refractive index Nd₃=1.72000of the third lens G3, there both the second lens G2 and the third lensG3 contact with the air.

Therefore, the exit surface of the second lens (surface number 3) cominginto contact with the fluid medium FM on the object side of the aperturestop STO has a concave surface so that the refraction angle of the fieldangle light beam is reduced. Thus, coma generated at the exit surface ofthe second lens is suppressed to be small.

The incident surface of the third lens (surface number 5) coming intocontact with the fluid medium FM on the image side of the aperture stopSTO is has a convex surface, so as to cancel the negative power given bythe exit surface of the second lens. Thus, field curvature and lateralchromatic aberration are corrected.

In addition, coma generated by the exit surface of the second lens iscorrected.

Thus, even if the fluid medium having a low refractive index is disposedinside the optical system close to a point symmetry structure,aberration of the field angle light beam can be appropriately corrected.Therefore, it is possible to realize the imaging optical system having avariable aperture stop diameter while maintaining high opticalperformance.

In addition, concerning such problem that the field angle light beam issignificantly refracted by the exit surface of the second lens cominginto contact with the air so that coma, astigmatism, lateral chromaticaberration, chromatic field curvature, or the like occurs, the imagingapparatus of this example has a further solution so as to realize goodaberration correction.

Specifically, the radius of curvature R₃=15.6214 (mm) of the exitsurface of the second lens (surface number 3) is set larger than thedistance d₃=0.2500 (mm) from the exit surface of the second lens to theaperture stop STO.

Thus, the refraction angle of each light beam at the exit surface of thesecond lens is reduced while avoiding vignetting of the field anglelight beam by the exit surface of the second lens.

In addition, the radius of curvature R₅=7.4031 (mm) of the incidentsurface of the third lens (surface number 5) is set smaller than theradius of curvature R₃=15.6214 (mm) of the exit surface of the secondlens (surface number 3).

In other words, a relationship between the radius of curvature Rf of thelens surface coming into contact with the fluid medium FM on the objectside of the aperture stop STO and the radius of curvature Rr of the lenssurface coming into contact with the fluid medium FM on the image sideof the aperture stop STO satisfies the following Expression (18).|R_(r)|<|R_(f)|  (18)

In this way, a radius of curvature smaller than that of the exit surfaceof the second lens is given to the incident surface of the third lens,and hence lateral chromatic aberration and chromatic field curvature canbe appropriately corrected.

In particular, a relationship between power φ_(f) of the lens surfacecoming into contact with the fluid medium FM on the object side of theaperture stop STO and power φ_(r) of the lens surface coming intocontact with the fluid medium FM on the image side of the aperture stopSTO satisfies the following Expression (19). Thus, lateral chromaticaberration and chromatic field curvature can be corrected with goodbalance.

$\begin{matrix}{{- 5} \leq \frac{\phi_{r}}{\phi_{f}} \leq {- 1}} & (19)\end{matrix}$

Here, N_(i+1) represents a refractive index of the medium on the imageside of the lens surface, N_(i) represents a refractive index of themedium on the object side of the lens surface, and R_(i) represents aradius of curvature of the lens surface. Then, power φ_(i) of eachsurface is expressed by the following Expression (20).

$\begin{matrix}{\phi_{i} = \frac{\left( {N_{i + 1} - N_{i}} \right)}{R_{i}}} & (20)\end{matrix}$

In the imaging apparatus of this example, power of the exit surface ofthe second lens is φ₃=−0.0351, power of the incident surface of thethird lens is φ₅=0.0973, and a ratio between the power of the exitsurface of the second lens and the power of the incident surface of thethird lens is φ₅/φ₃=−2.772.

Because the exit surface of the second lens and the incident surface ofthe third lens are structured to satisfy Expression (19), lateralchromatic aberration and field curvature can be corrected with goodbalance.

Thus, imaging performance of the field angle light beam is furtherimproved in the imaging apparatus having a variable aperture stopdiameter, a small F value, and a wide angle of field.

Table 30 shows the specifications of the imaging apparatus of thisexample.

TABLE 30 Focal length of imaging f_sys 3.600 (mm) optical system F valueF/# 1.20 Angle of field 2ω 120.0 (deg) Entire length L_sys 6.229 (mm)Distance from exit pupil d_pup 3.503 (mm) to image plane

The imaging apparatus of this example has a small F value of F/1.2, avery wide angle of field of 120.0 (degrees), and a compact size with theentire length of 6.229 (mm), which is an example of the imagingapparatus in which brightness, high resolution, a very wide angle offield, and a compact size are realized at the same time.

Table 31 shows values of Expressions (1), (2), and (4) of the imagingapparatus of this example.

TABLE 31 Conditional expression (1) f_sys/d_pup 1.03 Conditionalexpression (2) |R_img|/f_sys 1.02 Conditional expression (4)|R_img|/d_pup 1.05

The value of Expression (1) is 1.03 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemfrom the aperture stop to the image side can be close to a pointsymmetry structure, and hence coma, astigmatism, and lateral chromaticaberration can be appropriately corrected.

The value of Expression (2) is 1.02 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a wide angle of field of 120.0 (degrees).

When Expressions (1) and (2) are satisfied, focus adjustment can beperformed from infinity to a close distance only by changing thedistance between the imaging optical system and the image plane withoutchanging the image plane shape.

In addition, in the imaging apparatus of this embodiment, a radius ofcurvature of the image plane is set substantially equal to the distancefrom the exit pupil to the image plane of the imaging optical system.

The value of Expression (4) is 1.05 and satisfies the range ofExpression (4). Thus, the imaging optical system is close to a pointsymmetry structure, and hence coma, astigmatism, distortion, and lateralchromatic aberration are appropriately corrected. Further, focusadjustment can be performed while maintaining high resolution in a widefocus adjustment range from infinity to a close distance.

FIG. 35 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 36 illustrates a lateral aberrationdiagram thereof.

As illustrated in FIG. 35, spherical aberration, axial chromaticaberration, astigmatism, field curvature, distortion, and chromaticspherical aberration are appropriately corrected. Here, the chromaticspherical aberration is defined as a difference between the sphericalaberration amount of the reference wavelength (for example, d-line) andthe spherical aberration amount of each wavelength (for example, C-line,F-line, or g-line).

As illustrated in FIG. 36, good performance is obtained in each fieldangle light beam, and coma, field curvature, and lateral chromaticaberration are appropriately corrected. In particular, the effect ofthis embodiment can be sufficiently exerted on a light beam having alarge angle of field (for example, a field angle light beam having anangle of field ω=35 (degrees)), and hence good imaging performance isobtained with a small F value over a wide angle of field.

Next, an action of improving the peripheral darkening is described.

In the imaging optical system of the imaging apparatus of this example,the radius of curvature of the image plane is set substantially equal tothe focal length of the imaging optical system so that the focal lengthcan be substantially uniform over the full angle of field.

Thus, the peripheral light intensity ratio can be improved by the squareof cos ω.

The largest half angle of field in this example is ω=60.0 (degrees) sothat cos² ω is 0.25 in contrast to cos⁴ ω=0.0625. Thus, peripheral lightintensity can be improved by 4 times.

When Expression (2) is satisfied, it is possible to obtain a reasonableeffect.

Further, in the imaging optical system of the imaging apparatus of thisexample, the radius of curvature of the image plane is set substantiallyequal to the distance from the exit pupil to the image plane of theimaging optical system, and hence the incident angle to the image planecan be substantially orthogonal.

Thus, the peripheral light intensity ratio can be improved by the firstpower of cos ω.

The largest half angle of field in this example is ω=60.0 (degrees) sothat cos³ ω is 0.125 in contrast to cos⁴ ω=0.0625. Thus, peripherallight intensity can be improved by 2 times.

When Expression (4) is satisfied, it is possible to obtain a reasonableeffect.

When Expressions (2) and (4) are satisfied at the same time, theperipheral light intensity ratio can be improved by the third power ofcos ω, and the peripheral light intensity can be increased to be 8 timesthe conventional value.

Thus, because the peripheral light intensity ratio of the imagingoptical system having a wide angle of field can be significantlyimproved, it is possible to provide the imaging apparatus that can takea high quality image with high contrast and little noise over a wideangle of field.

As described above, using the effect of this embodiment, it is possibleto realize the imaging apparatus having good imaging performance over awide angle of field even at a small F value with a compact structure.

In addition, the peripheral darkening can be significantly improved, andhence it is possible to realize the imaging optical system that is verybright over a wide angle of field.

Thus, because the exposure time can be significantly shortened, it ispossible to provide the imaging apparatus that can take a high qualityimage in which blur due to shaking, image blur due to movement of theobject, and noise are appropriately reduced.

In addition, it is possible to provide an imaging optical system with acompact structure in which a defocused subject can be significantlyblurred.

Further, using the above-mentioned high performance imaging opticalsystem with the simple structure, focus adjustment can be performed withlittle deterioration of imaging performance in a wide range frominfinity to a close distance.

Example 9

An imaging optical system used in an imaging apparatus of this exampleincludes five lenses G1, G2, G3, G4, and G5 and the aperture stop STOdisposed in the fluid medium as illustrated in FIG. 37.

The imaging optical system includes, in order from the object side: thefirst lens G1 as a meniscus lens having a convex surface facing theobject side; the second lens G2 as a meniscus lens having a convexsurface facing the object side; the third lens G3 as a meniscus lenshaving a convex surface facing the object side; the aperture stop STO;the fourth lens G4 as a biconvex lens; and the fifth lens G5 as ameniscus lens having a convex surface facing the image side.

The aperture stop STO of the imaging apparatus of this example isdisposed in the air layer between the third lens G3 and the fourth lensG4, and the variable aperture stop can be disposed.

In the imaging apparatus according to this example, the image sensor ICDis formed into a sphere shape so as to form the curved image plane IMG.Thus, good imaging performance is realized over the entire region of theimage plane IMG.

In addition, IMG in FIG. 37 represents the image plane and the incidentsurface of the optical transmission unit OTM. The image plane is formedinto a sphere shape so as to form the curved image plane IMG. Thus, goodimaging performance is realized over the entire region of the imageplane IMG.

The optical transmission unit OTM of this example is an image fiberformed of bound optical fibers of a few micron pitch and has a role oftransmitting an image formed on the image plane of the imaging opticalsystem to the image sensor ICD.

The incident surface of the optical transmission unit OTM is formed intoa spherically curved shape, and the exit surface is formed as a flatsurface so as to be in intimate contact with the image sensor ICD forconnection. Thus, the imaging unit ICU is formed.

The incident surface shape of the optical transmission unit OTM isformed along the field curvature of the imaging optical system. Thus,good image formation is realized over the entire region of the imageplane IMG.

The optical transmission unit OTM is used in this example. However,compared with a structure in which the image sensor itself is formedinto a spherical surface shape, there is the advantage of easyproduction of the imaging unit ICU in which one surface of the opticaltransmission unit OTM is formed into a spherical surface shape while theother surface is connected to the image sensor ICD.

Table 32 shows a structure of the imaging apparatus of this example.

Surface number 1 is the incident surface of the first lens G1, surfacenumber 2 is the cemented surface between the exit surface of the firstlens G1 and the incident surface of the second lens G2, and surfacenumber 3 is the cemented surface between the exit surface of the secondlens G2 and the incident surface of the third lens G3. Surface number 4is the exit surface of the third lens G3 and is connected to the airlayer.

Surface number 5 is the aperture stop STO and is disposed in the airlayer.

Surface number 6 is the incident surface of the fourth lens G4, surfacenumber 7 is the cemented surface between the exit surface of the fourthlens G4 and the incident surface of the fifth lens G5, and surfacenumber 8 is the exit surface of the fifth lens G5.

Surface number 9 is the image plane IMG and is the incident surface ofthe optical transmission unit OTM of the imaging unit ICU. Further, theexit surface of the optical transmission unit OTM is connected to theimage sensor ICD.

In Table 32, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number.

TABLE 32 Surface number R d Nd νd 1 9.2950 2.3612 2.001100 23.6 2 5.03293.2825 1.726350 26.1 3 7.6974 1.4531 1.670939 55.7 4 43.5438 0.6507 Air5 (STO) Infinity 0.5000 Air 6 25.3784 4.2148 1.882997 40.8 7 −4.69405.4967 2.000800 25.0 8 −12.3234 4.3457 Air 9 (IMG) −12.4205

In the imaging apparatus of this example, the space between the thirdlens G3 and the fourth lens G4 is filled with air as the fluid mediumFM. The aperture stop STO is disposed in the air, and the aperture stopdiameter is variable.

The lens surface coming into contact with the air layer on the objectside of the aperture stop STO is the exit surface of the third lens(surface number 4), and the lens surface coming into contact with theair layer on the image side of the aperture stop STO is the incidentsurface of the fourth lens G4 (surface number 6).

The exit surface of the third lens has a shape of a concave surface, andthe incident surface of the fourth lens G4 has a shape of a convexsurface.

Thus, it is possible to provide the imaging apparatus having highimaging performance over a wide angle of field and a variable aperturestop diameter.

In addition, concerning such problem that the field angle light beam issignificantly refracted by the exit surface of the third lens cominginto contact with the air so that coma, astigmatism, lateral chromaticaberration, chromatic field curvature, or the like occurs, the imagingapparatus of this example has a further solution so as to realize goodaberration correction.

Specifically, the radius of curvature R₄=43.5438 (mm) of the exitsurface of the third lens is set larger than the distance d₄=0.6507 (mm)from the exit surface of the third lens to the aperture stop STO.

Thus, the refraction angle at the exit surface of the third lens isreduced while avoiding vignetting of the field angle light beam by theexit surface.

In addition, the radius of curvature R₆=25.3784 (mm) of the incidentsurface of the fourth lens is set smaller than the radius of curvatureR₄=43.5438 (mm) of the exit surface of the third lens. Thus, therelationship of Expression (18) is satisfied.

In this way, a radius of curvature smaller than that of the exit surfaceof the third lens is given to the incident surface of the fourth lens,and hence lateral chromatic aberration and chromatic field curvature canbe appropriately corrected.

Further, power of the exit surface of the third lens is φ₄=−0.0154,power of the incident surface of the fourth lens is φ₆=0.0348, and aratio between the power of the exit surface of the third lens and thepower of the incident surface of the fourth lens is φ₆/φ₄=−2.258.

Because the exit surface of the third lens and the incident surface ofthe fourth lens are structured to satisfy Expression (19), lateralchromatic aberration and field curvature can be corrected with goodbalance.

Thus, imaging performance of the field angle light beam is furtherimproved in the imaging apparatus having a variable aperture stopdiameter, a small F value, and a wide angle of field.

Further, Table 33 shows the specifications of the imaging apparatus ofthis example.

TABLE 33 Focal length of f_sys 11.997 (mm) imaging optical system Fvalue F/# 1.6 Angle of field 2ω 65.5 (deg) Entire length L_sys 17.959(mm) Distance from exit d_pup 14.060 (mm) pupil to image plane

The imaging apparatus of this example is an example of the imagingoptical system in which the aperture stop is disposed in the air layer,and the variable aperture stop is adopted.

With the simple structure of five lenses, the bright optical system ofF/1.6 is realized.

In addition, the entire length is 17.959 (mm) in contrast to the focallength 11.997 (mm) so that the compact optical system ofL_sys/f_sys=1.50 is realized.

Table 34 shows values of Expressions (1), (2), and (4) of the imagingapparatus of this example.

TABLE 34 Conditional expression (1) f_sys/d_pup 0.85 Conditionalexpression (2) |R_img|/f_sys 1.04 Conditional expression (4)|R_img|/d_pup 0.88

The value of Expression (1) is 0.85 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemin the image side of the aperture stop can be close to a point symmetrystructure, and hence coma, astigmatism, and lateral chromatic aberrationcan be appropriately corrected.

The value of Expression (2) is 1.04 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over an angle of field of 65.5 (degrees).

When Expressions (1) and (2) are satisfied, focus adjustment can beperformed from infinity to a close distance only by changing thedistance between the imaging optical system and the image plane withoutchanging the image plane shape.

The value of Expression (4) is 0.88 and satisfies the range ofExpression (4). Thus, the field curvature due to focus adjustment can besuppressed to be very small at an object distance in a wide range frominfinity to a close distance so that high resolution photography can beperformed.

In this way, also in this example, it is possible to realize the imagingapparatus having good imaging performance over a wide angle of fieldeven at a small F value with a compact structure.

FIG. 38 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 39 illustrates a lateral aberrationdiagram thereof.

As illustrated in FIG. 38, spherical aberration, axial chromaticaberration, astigmatism, field curvature, and chromatic sphericalaberration are appropriately corrected.

Because the spherical aberration and the chromatic spherical aberrationare appropriately corrected, good imaging performance is realized alsoat a small F value.

In addition, because astigmatism and field curvature are appropriatelycorrected, good imaging performance is realized also in a wide angle offield.

In particular, astigmatism is corrected, and the effect of thisembodiment is sufficiently exerted.

As illustrated in FIG. 39, coma, field curvature, and lateral chromaticaberration are appropriately corrected, and good performance is obtainedin each field angle light beam.

In particular, coma is corrected, and the effect of this embodiment issufficiently exerted.

Example 10

An imaging optical system used in an imaging apparatus of this exampleincludes four lenses G1, G2, G3, and G4 and the aperture stop STOdisposed in the fluid medium as illustrated in FIG. 40.

The imaging optical system includes, in order from the object side: thefirst lens G1 as a meniscus lens having a convex surface facing theobject side; the second lens G2 as a meniscus lens having a convexsurface facing the object side; the aperture stop STO; the third lens G3as a biconvex lens; and the fourth lens G4 as a meniscus lens having aconvex surface facing the image side.

Similarly in the imaging apparatus of this example, the aperture stopSTO is disposed in the air layer between the second lens G2 and thethird lens G3, and the variable aperture stop is disposed. The imagingunit ICU of this example is the same as that in Example 9. Table 35shows a structure of the imaging apparatus of this example. Surfacenumber 1 is the incident surface of the first lens G1 and has a rotationsymmetry aspherical shape expressed by the polynomial of Expression(11). Surface number 2 is the cemented surface between the exit surfaceof the first lens G1 and the incident surface of the second lens G2.Surface number 3 is the exit surface of the second lens G2 and has arotation symmetry aspherical shape expressed by the polynomial ofExpression (11). Surface number 4 is the aperture stop STO and isdisposed in the air layer. The surface number 5 is the incident surfaceof the third lens G3 and has a rotation symmetry aspherical shapeexpressed by the polynomial of Expression (11). The surface number 6 isthe cemented surface between the exit surface of the third lens G3 andthe incident surface of the fourth lens G4. Surface number 7 is the exitsurface of the fourth lens G4 and has a rotation symmetry asphericalshape expressed by the polynomial of Expression (11). Surface number 8is the image plane IMG, which is the incident surface of the opticaltransmission unit OTM. Further, the exit surface of the opticaltransmission unit OTM (not shown) is connected to the image sensor ICD.

In Table 35, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an. Abbe number. Note that, the surface with a mark “(a)” isan aspherical surface.

TABLE 35 Configuration table Surface number R d Nd νd 1 9.0343(a) 0.50002.00270 19.3 2 7.6693 4.7626 1.62230 53.2 3 52.9741(a) 1.7051 Air 4(STO) Flat 0.3000 Air surface 5 23.2147(a) 7.6142 1.69500 42.2 6 −5.22871.3812 1.92286 20.9 7 −11.4729(a) 3.6728 Air 8 (IMG) −12.4694

As to the imaging apparatus of this example, Table 36(A) showsaspherical surface coefficients of surface number 1. Table 36(B) showsaspherical surface coefficients of surface number 3. Table 36(C) showsaspherical surface coefficients of surface number 5. Table 36(D) showsaspherical surface coefficients of surface number 7.

TABLE 36(A) Aspherical surface coefficients (Surface number 1) ParameterSymbol Value Conic constant K −9.38334E−02 Fourth order coefficient A−4.58788E−06 Sixth order coefficient B −1.37765E−07 Eighth ordercoefficient C 1.61144E−09 Tenth order coefficient D −4.58504E−11

TABLE 36(B) Aspherical surface coefficients (Surface number 3) ParameterSymbol Value Conic constant K 2.56112E+01 Fourth order coefficient A1.25978E−05 Sixth order coefficient B −9.35781E−07 Eighth ordercoefficient C 1.11123E−08 Tenth order coefficient D −6.72938E−11

TABLE 36(C) Aspherical surface coefficients (Surface number 5) ParameterSymbol Value Conic constant K 9.31013E+00 Fourth order coefficient A−2.54505E−04 Sixth order coefficient B 3.67515E−08 Eighth ordercoefficient C −2.31857E−07 Tenth order coefficient D 7.60027E−09

TABLE 36(D) Aspherical surface coefficients (Surface number 7) ParameterSymbol Value Conic constant K −1.46966E−01 Fourth order coefficient A−8.44255E−05 Sixth order coefficient B −3.95820E−07 Eighth ordercoefficient C −4.20813E−08 Tenth order coefficient D −1.12533E−10

In the imaging apparatus of this example, the space between the secondlens G2 and the third lens G3 is filled with air as the fluid medium FM.The aperture stop STO is disposed in the air, and the aperture stopdiameter is variable.

The lens surface coming into contact with the air layer on the objectside of the aperture stop STO is the exit surface of the second lens(surface number 3), and the lens surface coming into contact with theair layer on the image side of the aperture stop STO is the incidentsurface of the third lens G3 (surface number 5).

Also in the imaging apparatus of this example, the exit surface of thesecond lens (surface number 3) is a concave surface, and the incidentsurface of the third lens G3 (surface number 5) is a convex surface.

Thus, it is possible to provide the imaging apparatus having highimaging performance over a wide angle of field and a variable aperturestop diameter.

In addition, concerning such problem that the field angle light beam issignificantly refracted by the exit surface of the second lens cominginto contact with the air so that coma, astigmatism, lateral chromaticaberration, chromatic field curvature, or the like occurs, the imagingapparatus of this example has a further solution so as to realize goodaberration correction.

Specifically, the radius of curvature R₃=52.9741 (mm) of the exitsurface of the second lens (surface number 3) is set larger than thedistance d₃=1.7051 (mm) from the exit surface of the second lens(surface number 3) to the aperture stop STO.

Thus, the refraction angle is reduced while avoiding vignetting of thefield angle light beam by the exit surface of the second lens.

In addition, the radius of curvature R₅=23.2147 (mm) of the incidentsurface of the third lens G3 (surface number 5) is set smaller than theradius of curvature R₃=52.9741 (mm) of the exit surface of the secondlens (surface number 3), and the following Expression (18) is satisfied.

In this way, a radius of curvature smaller than that of the exit surfaceof the second lens is given to the incident surface of the third lens,and hence lateral chromatic aberration and chromatic field curvature canbe appropriately corrected.

Further, power of the exit surface of the second lens is φ₃=−0.0117,power of the incident surface of the third lens is φ₅=0.0299, and aratio between the power of the exit surface of the second lens and thepower of the incident surface of the third lens is φ₅/φ₃=−2.549.

Because the exit surface of the third lens and the incident surface ofthe fourth lens are structured to satisfy Expression (19), lateralchromatic aberration and field curvature can be corrected with goodbalance.

Thus, imaging performance of the field angle light beam is furtherimproved in the imaging apparatus having a variable aperture stopdiameter, a small F value, and a wide angle of field.

In addition, in the imaging apparatus of this example, the distanced₅=0.3000 (mm) from the aperture stop STO to the incident surface of thethird lens G3 is set shorter than the distance d₃=1.7051 (mm) from theexit surface of the second lens to the aperture stop STO.

Therefore, lateral chromatic aberration can be corrected moreappropriately.

Thus, imaging performance of the field angle light beam can be improvedmore in the imaging apparatus having a small F value and a wide angle offield.

In addition, FIG. 41A shows an aspherical amount of surface number 1,FIG. 41B shows an aspherical amount of surface number 3, FIG. 42A showsan aspherical amount of surface number 5, and FIG. 42B shows anaspherical amount of surface number 7.

Here, the aspherical amount means a sag amount ΔZ_(ASP) that is adisplacement of the aspherical surface from the reference sphericalsurface to the optical axis direction, and is obtained by subtracting asag amount of the spherical surface from a sag amount of an asphericalsurface polynomial of Expression (11).

Specifically, the aspherical amount is expressed by the followingExpression (21).

$\begin{matrix}{{\Delta\; z_{ASP}} = {\left( {\frac{{cr}^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}} + {Ar}^{4} + {Br}^{6} + {Cr}^{8} + {Dr}^{10}} \right) - \left( \frac{{cr}^{2}}{1 + \sqrt{1 - {c^{2}r^{2}}}} \right)}} & (21)\end{matrix}$

The aspherical amount of surface number 1 is negative in the peripheryof the lens surface and is displaced from the reference sphericalsurface to the object side.

The aspherical amount of surface number 3 is positive in the peripheryof the lens surface and is displaced from the reference sphericalsurface to the object side. The aspherical amount of surface number 5 isnegative in the periphery of the lens surface and is displaced from thereference spherical surface to the object side.

The aspherical amount of surface number 7 is negative in the peripheryof the lens surface and is displaced from the reference sphericalsurface to the object side.

By these aspherical shapes, more appropriate imaging performance isobtained.

In particular, the exit surface of the second lens (surface number 3) isa concave surface, the aspherical shape displaced from the referencespherical surface to the image side in the periphery of the lens surface(having a positive aspherical amount) is given, and a negative powercomponent is added to the periphery. Thus, aberration generated by theair layer can be appropriately corrected.

Further, the incident surface of the third lens G3 (surface number 5) isa convex surface, the aspherical shape displaced from the referencespherical surface to the object side in the periphery of the lenssurface (having a negative aspherical amount) is given, and a negativepower component is added to the periphery. Thus, aberration generated bythe air layer can be appropriately corrected.

Further, when the configurations of both the lenses are realized at thesame time, aberration can be corrected more appropriately so that highimaging performance can be obtained.

Table 37 shows the specifications of the imaging apparatus of thisexample.

TABLE 37 Focal length of f_sys 11.997 (mm) imaging optical system Fvalue F/# 1.20 Angle of field 2ω 70.0 (deg) Entire length L_sys 16.263(mm) Distance from exit d_pup 12.968 (mm) pupil to image plane

The imaging apparatus of this example has a remarkably small F value ofF/1.2, a wide angle of field of 70.0 (degrees), and a compact size withthe entire length of 16.263 (mm), which is an example of the imagingapparatus in which brightness, high resolution, and a compact size arerealized at the same time.

Table 38 shows values of Expressions (1), (2), and (4) of the imagingapparatus of this example.

TABLE 38 Conditional expression (1) f_sys/d_pup 1.07 Conditionalexpression (2) |R_img|/f_sys 1.04 Conditional expression (4)|R_img|/d_pup 1.11

The value of Expression (1) is 1.07 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemfrom the aperture stop to the image side can be close to a pointsymmetry structure, and hence coma, astigmatism, distortion, and lateralchromatic aberration can be appropriately corrected.

The value of Expression (2) is 1.04 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a wide angle of field of 70.0 (degrees).

The value of Expression (4) is 1.11 and satisfies the range ofExpression (4). Thus, the imaging optical system is close to a pointsymmetry structure, and hence coma, astigmatism, distortion, and lateralchromatic aberration are appropriately corrected.

Further, in the imaging apparatus of this example, the distance betweenthe imaging optical system and the image plane is changed so as toperform focus adjustment. Because Expression (4) is satisfied, focusadjustment can be performed while maintaining high resolution in a widefocus adjustment range from infinity to a close distance.

FIG. 43 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 44 illustrates a lateral aberrationdiagram thereof. As illustrated in FIG. 43, spherical aberration, axialchromatic aberration, astigmatism, field curvature, and chromaticspherical aberration are appropriately corrected. In particular, thelight beam can be condensed on the image plane in the entire range froma low incident height light ray to a high incident height light ray.Thus, spherical aberration can be very appropriately corrected.

In addition, axial chromatic aberration and chromatic sphericalaberration are also very appropriately corrected, and hence high imagingperformance can be obtained.

As illustrated in FIG. 44, coma, field curvature, and lateral chromaticaberration are appropriately corrected, and good performance is obtainedin each field angle light beam.

As in this example, both the lens surface closest to the object side andthe lens surface closest to the image side can be aspherical surfaces towhich the aspherical amount displaced from the reference sphericalsurface to the outside of the imaging optical system in the periphery ofthe lens surface is given. Thus, spherical aberration can be correctedwith high accuracy over a wide angle of field.

Example 11

An imaging optical system used in an imaging apparatus of this exampleincludes four lenses G1, G2, G3, and G4 and the aperture stop STOdisposed in the fluid medium as illustrated in FIG. 45.

The imaging optical system includes, in order from the object side: thefirst lens G1 as a meniscus lens having a convex surface facing theobject side; the second lens G2 as a meniscus lens having a convexsurface facing the object side; the third lens G3 as a biconvex lenshaving a convex surface facing the image side; and the fourth lens G4 asa meniscus lens having a convex surface facing the image side.

In addition, the space between the second lens G2 and the third lens G3is filled with silicone oil as the fluid medium FM, and the aperturestop STO is disposed therein. The imaging unit ICU of this example isthe same as that in Example 9.

Table 39 shows a structure of the imaging apparatus of this example.

Surface number 1 is the incident surface of the first lens G1, andsurface number 2 is the cemented surface between the exit surface of thefirst lens G1 and the incident surface of the second lens G2. Surfacenumber 3 is the exit surface of the second lens G2 having a rotationsymmetry aspherical shape expressed by the polynomial of Expression(11). In addition, surface number 3 is the lens surface coming intocontact with the fluid medium in which the aperture stop is disposed onthe object side than of aperture stop.

Surface number 4 is the aperture stop STO and is disposed in the siliconoil. Surface number 5 is the incident surface of the third lens G3having a rotation symmetry aspherical shape expressed by the polynomialof Expression (11). In addition, the surface number 5 is the lenssurface coming into contact with the fluid medium in which the aperturestop is disposed on the image side than of aperture stop.

Surface number 6 is the cemented surface between the exit surface of thethird lens G3 and the incident surface of the fourth lens G4. Surfacenumber 7 is the exit surface of the fourth lens G4 having a rotationsymmetry aspherical shape expressed by the polynomial of Expression(11). Surface number 8 is the image plane IMG, which is the incidentsurface of the curved image sensor.

In Table 39, R represents a radius of curvature resents a surfaceinterval (mm), Nd represent-line refractive index, and νd represents anAbbe number. Note that, the surface with a mark “(a)” is an asphericalsurface.

TABLE 39 Configuration table Surface number R d Nd νd 1 11.1500 5.68612.00270 19.3 2 5.6510 3.0063 1.88300 40.8 3 25.6855(a) 1.0000 1.4040050.0 4 (STO) Flat 0.5000 1.40400 50.0 surface 5 20.4801(a) 3.49421.87801 38.5 6 −4.9914 6.0698 2.00060 25.5 7 −12.0967(a) 2.6401 Air 8(IMG) −13.1649

As to the imaging apparatus of this example, Table 40(A) showsaspherical surface coefficients of surface number 3. Table 40(B) showsaspherical surface coefficients of surface number 5. Table 40(C) showsaspherical surface coefficients of surface number 7.

TABLE 40(A) Aspherical surface coefficients (Surface number 3) ParameterSymbol Value Conic constant K −7.80416E−01 Fourth order coefficient A1.25565E−04 Sixth order coefficient B −7.06450E−07 Eighth ordercoefficient C −2.54125E−07 Tenth order coefficient D 6.69057E−09

TABLE 40(B) Aspherical surface coefficients (Surface number 5) ParameterSymbol Value Conic constant K 1.26266E+00 Fourth order coefficient A−2.60614E−04 Sixth order coefficient B −1.41325E−05 Eighth ordercoefficient C 1.21573E−06 Tenth order coefficient D −4.53144E−08

TABLE 40(C) Aspherical surface coefficients (Surface number 7) ParameterSymbol Value Conic constant K −9.42506E−01 Fourth order coefficient A−6.45473E−05 Sixth order coefficient B −2.93067E−07 Eighth ordercoefficient C 2.59828E−09 Tenth order coefficient D −2.85562E−10

In the imaging apparatus of this example, the space between the secondlens G2 and the third lens G3 is filled with silicone oil as the fluidmedium FM. The aperture stop STO is disposed in the silicone oil, andthe aperture stop diameter is variable.

The refractive index of silicone oil is Nd=1.404, which is higher thanthe refractive index of air and is close to the refractive index of theoptical glass of the second lens and the third lens coming into contactwith the silicone oil.

Therefore, it is possible to decrease the refraction angle of the fieldangle light beam on the exit surface of the second lens or the incidentsurface of the third lens, which can give the effect of suppressinggenerated aberration to be small. The silicone oil is used as the fluidmedium FM in this example, but it is possible to use water. Therefractive index of water is Nd=1.333, which is higher than therefractive index Nd=1.000 of air and is close to the refractive index ofthe optical glass. Therefore, it is possible to give the substantiallysame effect as the silicone oil.

In this way, the fluid medium FM in which the aperture stop is disposedis preferred to have the refractive index Nd>1.000. Thus, aberration canbe suppressed to be small, and it is effective to realize highresolution.

In the imaging apparatus of this example, the lens surface disposedcloser to the object side than the aperture stop and coming into contactwith the fluid medium is the exit surface of the second lens G2 (surfacenumber 3), and the lens surface closer to the image side than theaperture stop and coming into contact with the fluid medium is theincident surface of the third lens G3 (surface number 5).

In the imaging apparatus of this example, too, the exit surface of thesecond lens (surface number 3) has a concave surface, and the incidentsurface of the third lens G3 (surface number 5) is set to have a convexsurface.

Thus, it is possible to provide the imaging apparatus having highimaging performance over a wide angle of field and a variable aperturestop diameter.

In addition, concerning such problem that the field angle light beam issignificantly refracted by the exit surface of the second lens cominginto contact with the silicone oil so that coma, astigmatism, lateralchromatic aberration, chromatic field curvature, or the like occurs, theimaging apparatus of this example has a further solution so as torealize good aberration correction.

Specifically, the radius of curvature R₃=25.6855 (mm) of the exitsurface of the second lens (surface number 3) is set larger than thedistance d₃=1.0000 (mm) from the exit surface of the second lens(surface number 3) to the aperture stop STO. Thus, the refraction angleis reduced while avoiding vignetting of the field angle light beam bythe exit surface of the second lens.

In addition, the radius of curvature R₅=20.4801 (mm) of the incidentsurface of the third lens G3 (surface number 5) is set smaller than theradius of curvature R₃=25.6855 (mm) of the exit surface of the secondlens (surface number 3), and the following Expression (18) is satisfied.

In this way, a radius of curvature smaller than that of the exit surfaceof the second lens is given to the incident surface of the third lens,and hence lateral chromatic aberration and chromatic field-curvature canbe appropriately corrected.

Further, power of the exit surface of the second lens is φ₃=−0.0186,power of the incident surface of the third lens is φ₅=0.0231, and aratio between the power of the exit surface of the second lens and thepower of the incident surface of the third lens is φ₅/φ₃=−1.241.

Because the exit surface of the second lens G2 and the incident surfaceof the third lens G3 are structured to satisfy Expression (19), lateralchromatic aberration and field curvature can be corrected with goodbalance.

Thus, imaging performance of the field angle light beam is furtherimproved in the imaging apparatus having a variable aperture stopdiameter, a small F value, and a wide angle of field.

In addition, in the imaging apparatus of this example, the distanced₅=0.500 (mm) from the aperture stop STO to the incident surface of thethird lens G3 is set shorter than the distance d₃=1.000 (mm) from theexit surface of the second lens to the aperture stop STO.

Therefore, lateral chromatic aberration can be corrected moreappropriately.

Thus, imaging performance of the field angle light beam can be improvedmore in the imaging apparatus having a small F value and a wide angle offield.

In this way, stronger power is given to the incident surface of thethird lens G3 than to the exit surface of the second lens, and hencelateral chromatic aberration and chromatic field curvature can beappropriately corrected.

In addition, in the imaging apparatus of this example, the distanced₅=0.5000 (mm) from the aperture stop STO to the incident surface of thethird lens G3 is set shorter than the distance d₃=1.0000 (mm) from theexit surface of the second lens to the aperture stop STO.

Therefore, coma as well as lateral chromatic aberration can be correctedappropriately.

Thus, imaging performance of the field angle light beam can be improvedmore in the imaging apparatus having a small F value and a wide angle offield.

In addition, FIG. 46A shows the aspherical amount of surface number 3,FIG. 46B shows the aspherical amount of surface number 5, and FIG. 47shows the aspherical amount of surface number 7.

The aspherical amount of surface number 3 is positive in the peripheryof the lens surface and has an aspherical shape displaced from thereference spherical surface to the image side. The aspherical amount ofsurface number 5 is negative in the periphery of the lens surface andhas an aspherical shape displaced from the reference spherical surfaceto the object side.

The aspherical amount of surface number 7 is negative in the peripheryof the lens surface and has an aspherical shape displaced from thereference spherical surface to the object side.

By these aspherical shapes, more appropriate imaging performance isobtained.

In particular, the exit surface of the second lens (surface number 3)has a concave surface, the aspherical shape displaced from the referencespherical surface to the image side in the periphery of the lens surface(having a positive aspherical amount) is given, and a negative powercomponent is added to the periphery. Thus, aberration generated by thesilicon oil layer can be appropriately corrected.

Further, the incident surface of the third lens G3 (surface number 5)has a convex surface having the aspherical shape displaced from thereference spherical surface to the object side in the periphery of thelens surface (having a negative aspherical amount), and a negative powercomponent is added to the periphery. Thus, aberration generated by thesilicon oil layer can be more appropriately corrected.

Further, when the configurations of both the lenses are realized at thesame time, aberration can be corrected more appropriately so that highimaging performance can be obtained.

Table 43 shows the specifications of the imaging apparatus of thisexample.

TABLE 43 Focal length of f_sys 3.600 (mm) imaging optical system F valueF/# 1.20 Angle of field 2ω 120.0 (deg) Entire length L_sys 6.044 (mm)Distance from exit d_pup 3.616 (mm) pupil to image plane

The imaging apparatus of this example has a small F value of F/1.2, avery wide angle of field of 120.0 (degrees), and a compact size with theentire length of 6.044 (mm), which is an example of the imagingapparatus in which brightness, high resolution, a very wide angle offield, and a compact size are realized at the same time.

Table 44 shows values of Expressions (1), (2), and (4) of the imagingapparatus of this example.

TABLE 44 Conditional expression (1) f_sys/d_pup 0.96 Conditionalexpression (2) |R_img|/f_sys 1.01 Conditional expression (4)|R_img|/d_pup 0.97

The value of Expression (1) is 0.96 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemin the image side of the aperture stop can be close to a point symmetrystructure, and hence coma, astigmatism, distortion, and lateralchromatic aberration can be appropriately corrected.

The value of Expression (2) is 1.01 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a wide angle of field of 120.0 (degrees).

The value of Expression (4) is 0.97 and satisfies the range ofExpression (4). Thus, the imaging optical system is close to a pointsymmetry structure, and hence coma, astigmatism, distortion, and lateralchromatic aberration are appropriately corrected.

Further, in the imaging apparatus of this example, the distance betweenthe imaging optical system and the image plane is changed so as toperform focus adjustment. Because Expression (4) is satisfied, focusadjustment can be performed while maintaining high resolution in a widefocus adjustment range from infinity to a close distance.

FIG. 48 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 49 illustrates a lateral aberrationdiagram thereof.

As illustrated in FIG. 48, spherical aberration, axial chromaticaberration, astigmatism, field curvature, and chromatic sphericalaberration are very appropriately corrected.

In particular, the light beam in the entire region from a low incidentlight beam height to a high incident light beam height can be condensedon the image plane, and hence spherical aberration can be veryappropriately corrected.

In addition, axial chromatic aberration and chromatic sphericalaberration are also very appropriately corrected so that high imagingperformance is obtained.

As illustrated in FIG. 49, good performance is obtained in each fieldangle light beam, and coma, field curvature, and lateral chromaticaberration are very appropriately corrected.

As in this example, both the lens surface closest to the object side andthe lens surface closest to the image side are formed as asphericalsurfaces to which the aspherical amount displaced from the referencespherical surface to the outside of the imaging optical system in theperiphery of the lens surface is given. Thus, spherical aberration canbe corrected with high accuracy over a wide angle of field.

(Fourth Embodiment)

This embodiment has the structure in which at least one of the lenssurface closest to the object side and the lens surface closest to theimage side of the imaging optical system is formed as the asphericalsurface having the aspherical amount displaced from the referencespherical surface to the outside of the imaging optical system in theperiphery of the lens surface. Thus, spherical aberration can beappropriately corrected also in a bright optical system having a wideangle of field.

Next, description is given of an action of the structure in which atleast one of the lens surface closest to the object side and the lenssurface closest to the image side of the imaging optical system isformed as the aspherical surface having the aspherical amount displacedfrom the reference spherical surface to the outside of the imagingoptical system in the periphery of the lens surface.

The aspherical surface having the aspherical amount displaced from thereference spherical surface to the outside of the imaging optical systemin the periphery of the lens surface mainly acts on correction ofspherical aberration.

The imaging optical system has positive power as a whole, and sphericalaberration usually becomes “under”.

In view of the optical path length from the object point to the imagepoint, this is caused by a factor that the optical path length of thelight beam in a high incident height position is shorter compared withthat of the axial light.

In addition, in view of the wave front, this is caused by a factor thatthe phase of the light beam is advanced in a high incident heightposition compared with that on the optical axis.

Therefore, at least one of the lens surface closest to the object sideand the lens surface closest to the image side of the imaging opticalsystem is formed of the aspherical surface having the aspherical amountdisplaced from the reference spherical surface to the outside of theimaging optical system in the periphery of the lens surface.

The lens surface closest to the object side or the lens surface closestto the image side in the imaging optical system is the outermost lenssurface among the lens surfaces included in the imaging optical system.The inside of the lens surface is filled with the optical glass, and theoutside of the lens surface is filled with the air.

In general, the refractive index of the optical glass is Nd=1.45 to2.15, which is higher than the refractive index of the air, Nd=1.0.

In this case, a part of the optical path of the light beam passingthrough the periphery of the lens surface is replaced from the air tothe optical glass by the aspherical surface having the aspherical amountdisplaced from the reference spherical surface to the outside of theimaging optical system in the periphery of the lens surface. Thus, theoptical path length can be substantially increased. Alternatively, thephase of the wave front can be delayed. Thus, spherical aberration canbe appropriately corrected.

In addition, in view of the power, it is possible to constitute theaspherical surface in which the power of the periphery of the lenssurface is shifted in the negative direction by the aspherical surfacehaving the aspherical amount displaced from the reference sphericalsurface to the outside of the imaging optical system in the periphery ofthe lens surface.

If the reference spherical surface has positive power, it is possible tostructure the aspherical surface in which the positive power in theperiphery is reduced compared with that on the optical axis.

Thus, the power received by the light ray in a high incident heightposition can be relatively reduced to the power received by principalray, and hence spherical aberration in the “under” state can beappropriately corrected.

FIG. 84 is an optical path diagram schematically illustrating a mannerof image formation by the axial light in the imaging apparatus of thisembodiment, and FIG. 85 is an optical path diagram schematicallyillustrating a manner of image formation by the field angle light beam.

FIGS. 84 and 85 schematically illustrate a manner in which a field anglelight beam BEM from the object point PNT_(OBJ) on the object plane OBJforms an image at the image point PNT_(IMG) on the image plane IMG bythe imaging optical system SYS.

As illustrated in FIG. 84, the axial light is defined as a case wherethe object point PNT_(OBJ) is on the optical axis AXI of the imagingoptical system SYS. AS illustrated in FIG. 85, the field angle lightbeam is defined as a case where the object point PNT_(OBJ) is not on theoptical axis AXI of the imaging optical system SYS.

The light beam widths of the axial light and the field angle light beamare limited by the aperture stop STO. The light ray passing through anopening center STO_(CNT) of the aperture stop is defined as a principalray RAY_(PRI), the light ray passing through an opening upper endSTO_(UP) is defined as an upper ray RAY_(UP), and the light ray passingthrough an opening lower end STO_(LOW) is defined as a lower rayRAY_(LOW).

In FIG. 84, the axial light BEM_(ON) is refracted by a lens surfaceR_(MSTOBJ) closest to the object side, and its light beam width islimited by the aperture stop STO. Then, the axial light BEM_(ON) isrefracted by a lens surface R_(MSTIMG) closest to the image side so asto form an image on the image plane IMG.

As to reach positions of the light rays on the lens surface R_(MSTOBJ)closest to the object side, the principal ray RAY_(PRI) is on theoptical axis AXI, the upper ray RAY_(UP) is close to the upper sideperiphery, and the lower ray RAY_(LOW) is close to the lower sideperiphery. The lens surface R_(MSTOBJ) closest to the object side is thesurface having a largest light beam width in the imaging optical systemSYS.

Spherical aberration has a feature of being vulnerable to the influenceof power of the surface having a high incident height h (surface havinga large light beam width). According to the third order aberrationcoefficient, spherical aberration is proportional to the fourth power ofthe incident height h and is considerably affected by power of the lenssurface.

Therefore, when the lens surface R_(MSTOBJ) closest to the object sideis formed of the aspherical surface, the action of the asphericalsurface can be effectively exerted.

In addition, by using the aspherical surface having power decreased morein the periphery than on the optical axis, power for the upper rayRAY_(UP) having a high incident height or power for the lower rayRAY_(LOW) can be decreased more than that on the optical axis.Therefore, the spherical aberration to be “under” can be appropriatelycorrected.

In addition, because the influence to spherical aberration is large, thespherical aberration amount to be given can be controlled to be small.

As illustrated in FIG. 85, when the object point PNT_(OBJ) is below theoptical axis of the imaging optical system SYS, the optical path lengthof the upper ray RAY_(UP) (from the object point PNT_(OBJ) to theopening upper end STO_(UP) of the aperture stop) is longer than theoptical path length of the principal ray RAY_(PRI) (from the objectpoint PNT_(OBJ) to the opening center STO_(CNT) of the aperture stop) inthe field angle light beam BEM.

Therefore, there is a problem in that the incident height in thedirection along the principal ray RAY_(PRI) is higher than the incidentheight of the axial light in the light beam closer to the upper rayRAY_(UP) than the principal ray RAY_(PRI), which causes large sphericalaberration. This problem becomes more conspicuous as the angle of fieldbecomes wider.

On the other hand, the reach point of the upper ray RAY_(UP) of thefield angle light beam BEM on the lens surface R_(MSTIMG) closest to theimage side is closer to the periphery of the lens surface R_(MSTIMG)closest to the image side than the reach point of the principal rayRAY_(PRI).

Therefore, the lens surface R_(MSTIMG) closest to the image side isformed as the aspherical surface having power decreased more in theperiphery than on the optical axis. Then, it is possible to constitutethe lens surface that can give weaker power to the light beam closer tothe upper ray RAY_(UP) than to the principal ray RAY_(PRI).

Thus, it is possible to appropriately correct spherical aberrationgenerated significantly in the light beam closer to the upper rayRAY_(UP) than the principal ray RAY_(PRI) of the field angle light beam.

In addition, spherical aberration occurs also in the light beam closerto the lower ray RAY_(LOW) than the principal ray RAY_(PRI) of the fieldangle light beam.

The reach point of the lower ray RAY_(LOW) of the field angle light beamBEM on the lens surface R_(MSTOBJ) closest to the object side is closerto the periphery of the lens surface R_(MSTOBJ) closest to the objectside than the reach point of the principal ray RAY_(PRI).

Therefore, the lens surface R_(MSTOBJ) closest to the object side isformed as the aspherical surface having power decreased more in theperiphery than on the optical axis. Then, it is possible to constitutethe lens surface that can give weaker power to the light beam closer tothe lower ray RAY_(LOW) than to the principal ray RAY_(PRI).

Thus, it is possible to appropriately correct spherical aberrationgenerated in the light beam closer to the lower ray RAY_(LOW) than theprincipal ray RAY_(PRI) of the field angle light beam.

Further, when both the lens surface closest to the object side and thelens surface closest to the image side are formed as the asphericalsurfaces having power reduced more in the periphery than on the opticalaxis, it is possible to realize the structure optimal for the axiallight, the light beam closer to the upper ray than the principal ray ofthe field angle light beam, and the light beam closer to the lower raythan the principal ray of the field angle light beam.

In the imaging optical system having a small F value, it is difficult tocorrect spherical aberration only by the spherical surface lens.However, according to this embodiment, spherical aberration can beappropriately corrected.

In particular, in the imaging apparatus using a very bright imagingoptical system having F/1.4 or smaller, imaging performance can besignificantly improved by correcting spherical aberration as in thisembodiment.

When the cemented surface is formed as the aspherical surface, there isa disadvantage that it is difficult to form the two surfaces into thesame aspherical shape. If the lens surface closest to the object side orthe lens surface closest to the image side of the imaging optical systemis formed as the aspherical surface, there is an advantage thatproduction becomes easy.

In the following, an example of this embodiment is described.

Example 12

In Example 12, a structural example of the imaging apparatus to whichthis embodiment is applied is described.

An imaging optical system used in an imaging apparatus of this exampleincludes three lenses G1, G2, and G3 and the aperture stop STO asillustrated in FIG. 50.

The imaging optical system includes, in order from the object side: afirst lens G1 as a plano-convex lens having a convex surface facing theobject side; a second lens G2 as a plano-convex lens having a convexsurface facing the image side; and a third lens G3 as a meniscus lenshaving a convex surface facing the image side.

The exit surface of the first lens G1 is cemented to the incidentsurface of the second lens G2, and the light blocking member is disposedin the non-effective part of the cemented surface so as to constitutethe aperture stop STO.

In FIG. 50, IMG represents the image plane.

As illustrated in FIG. 50, in the imaging apparatus according to thisexample, the incident surface of the optical transmission unit OTMformed into a sphere shape is used as the image plane IMG, and thecurved shape of the image plane is formed along the field curvature ofthe imaging optical system. Thus, good imaging performance is realizedover the entire region of the image plane IMG.

The optical transmission unit OTM of the imaging apparatus according tothis example is an image fiber formed of bound optical fibers of a fewmicron pitch and has a role of transmitting an image formed on the imageplane to the image sensor ICD.

The exit surface of the optical transmission unit OTM is formed to be aflat surface so as to be in intimate contact with the image sensor ICDfor connection. Thus, an image is transmitted to the image sensor ICD.

In this way, in the imaging apparatus of this example, the opticaltransmission unit OTM and the image sensor ICD constitute the imagingunit ICU.

Table 45 shows a structure of the imaging apparatus of this example.

Surface number 1 is the incident surface of the first lens G1, surfacenumber 2 is the cemented surface between the exit surface of the firstlens G1 and the second lens G2, surface number 3 is the cemented surfacebetween the exit surface of the second lens G2 and the incident surfaceof the third lens G3, and surface number 4 is the exit surface of thethird lens G3.

The light blocking member is disposed in the non-effective part in theplane of the surface number 2 between the exit surface of the first lensG1 and the second lens G2 indicated by surface number 2, and hence theaperture stop STO is constituted.

Surface number 5 is the image plane IMG, which is the incident surfaceof the optical transmission unit OTM. Further, the exit surface of theoptical transmission unit OTM (not shown) is connected to the imagesensor ICD so as to constitute the imaging unit ICU.

In Table 45, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number. Note that, the surface with a mark “(a)” isan aspherical surface.

TABLE 45 Configuration table Surface number R d Nd νd 1 3.1146(a) 3.06611.87801 38.5 2 (STO) Flat 1.1017 1.87801 38.5 surface 3 −1.0868 2.06142.00520 21.0 4 −3.2821 0.4524 5 (IMG) −3.6698

The aspherical surface of the imaging apparatus of this example isformed as the rotation symmetry aspherical surface whose center is theoptical axis, and is expressed by the polynomial of Expression (11).

The aspherical surface coefficients of the first surface of the imagingapparatus of this example are shown in Table 46.

TABLE 46 Aspherical surface coefficients (Surface number 1) ParameterSymbol Value Conic constant K −3.58921E−03 Fourth order coefficient A−5.87301E−05 Sixth order coefficient B 5.16920E−06 Eighth ordercoefficient C 0.00000E+00 Tenth order coefficient D 0.00000E+00

When the first order differential of the aspherical surface polynomialof Expression (11) by the distance r from the optical axis in the radialdirection is calculated, the first order differential value isdetermined by Expression (22).

$\begin{matrix}{{\frac{\partial\;}{\partial r}z} = {\frac{cr}{\sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}} + {4{Ar}^{3}} + {6{Br}^{5}} + {8{Cr}^{7}} + {10{Dr}^{9}} + \ldots}} & (22)\end{matrix}$

This first order differential value indicates a gradient of the lenssurface.

Further, when the second order differential of the aspherical surfacepolynomial of Expression (11) by the distance r from the optical axis inthe radial direction is calculated, the second order differential valueis determined by Expression (23).

$\begin{matrix}{{\frac{\partial^{2}\;}{\partial r^{2}}z} = {\frac{c}{\left\lbrack {1 - {\left( {1 + k} \right)c^{2}r^{2}}} \right\rbrack^{\frac{3}{2}}} + {12{Ar}^{2}} + {30{Br}^{4}} + {56{Cr}^{6}} + {90{Dr}^{7}} + \ldots}} & (23)\end{matrix}$

This second order differential value indicates a differential value ofthe gradient of the lens surface, namely the curvature in the radialdirection, which has a relationship with power φ_(r) as expressed byExpression (24).

$\begin{matrix}{\phi_{r} = {\left( {N^{\prime} - N} \right) \cdot \left( {\frac{\partial^{2}\;}{\partial r^{2}}z} \right)}} & (24)\end{matrix}$

Here, N represents a refractive index of a medium on the object side ofthe lens surface and N′ represents a refractive index of a medium on theimage side of the lens surface.

In the imaging apparatus of this example, only the lens surface closestto the object side among lens surfaces in the imaging optical system isformed as the aspherical surface.

FIG. 51A shows an aspherical surface of the lens surface closest to theobject side, and FIG. 51B shows an aspherical amount of the lens surfaceclosest to the object side. In addition, FIG. 52A shows a second orderdifferential value of the aspherical surface and the reference sphericalsurface, and FIG. 52B shows a second order differential value of theaspherical component.

As shown in FIG. 51A, the lens surface closest to the object side inthis example is a lens surface having a sag amount increasing in thepositive direction from the optical axis toward the periphery and aconvex surface facing the object side.

Note that, the sag amount means a displacement amount to the opticalaxis direction, which indicates how much other positions on the lenssurface is displaced to the optical axis direction with respect to theposition on the optical axis in FIG. 51A. In addition, the referencespherical surface is a spherical surface having a radius of curvatureR=3.1146 (mm) and a convex surface facing the object side.

FIG. 51B shows an aspherical amount. The aspherical amount means a sagamount ΔZ_(ASP) of the aspherical surface displaced from the referencecurved surface to the optical axis direction, which is calculated bysubtracting the sag amount of the spherical surface from the sag amountof the aspherical surface polynomial of Expression (11). Specifically,the aspherical amount is expressed by Expression (21).

As shown in FIG. 51B, in this example, the aspherical amount isdisplaced in the negative direction, and the aspherical surface isdisplaced from the reference spherical surface to the object side,namely to the outside of the imaging optical system.

Then, the aspherical amount of displacement of the imaging opticalsystem to the outside is increased gradually as being away from theoptical axis, and the largest aspherical amount is given in theperiphery of the lens surface.

FIG. 52A shows a second order differential value of the asphericalsurface by a solid line and a second order differential value of thereference spherical surface by a broken line.

Both the second order differential value of the aspherical surface andthe second order differential value of the reference spherical surfaceare increased gradually in the positive direction as being away from theoptical axis.

In addition, FIG. 52B shows the second order differential value of theaspherical component. This is obtained by subtracting the second orderdifferential value of the reference spherical surface from the secondorder differential value of the aspherical surface.

The second order differential value of the aspherical component isincreased gradually in the negative direction as being away from theoptical axis.

In this way, the aspherical component having a negative second orderdifferential value is given to the reference spherical surface having apositive second order differential value, and hence the second orderdifferential value in the periphery of the lens surface is reduced to besmaller than that of the reference spherical surface.

Expression (24) indicates a relationship between the second orderdifferential value and the power.

On the lens surface closest to the object side of the imaging opticalsystem, the medium on the object side of the lens surface is air havingN=1.0000, and the medium on the image side of the lens surface isoptical glass having N′=1.87801. Therefore, (N′−N) has a positive value.

Therefore, the lens surface closest to the object side is formed as thelens surface shape having positive power on the optical axis which isgradually decreased as being away from the optical axis.

Thus, spherical aberration can be appropriately corrected.

FIG. 53 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 54 illustrates a lateral aberrationdiagram thereof.

As illustrated in FIG. 53, spherical aberration, axial chromaticaberration, astigmatism, field curvature, and chromatic sphericalaberration are appropriately corrected. Here, the chromatic sphericalaberration is defined as a difference between the spherical aberrationamount of the reference wavelength (for example, d-line) and thespherical aberration amount of each wavelength (for example, C-line,F-line, g-line, or the like).

In particular, the light beam in the entire region from a low incidentlight beam height to a high incident light beam height can be condensedon the image plane, and hence spherical aberration can be veryappropriately corrected.

In addition, axial chromatic aberration and chromatic sphericalaberration are also very appropriately corrected so that high imagingperformance is obtained.

As illustrated in FIG. 54, good performance is obtained in each fieldangle light beam, and coma, field curvature, and lateral chromaticaberration are appropriately corrected.

Table 47 shows the specifications of the imaging apparatus of thisexample.

TABLE 47 Focal length of f_sys 3.600 (mm) imaging optical system F valueF/# 1.20 Angle of field 2ω 120.0 (deg) Entire length L_sys 6.229 (mm)Distance from exit d_pup 3.503 (mm) pupil to image plane

The imaging apparatus of this example has a small F value of F/1.2, avery wide angle of field of 120.0 (degrees), and a compact size with theentire length of 6.229 (mm), which is an example of the imagingapparatus in which brightness, high resolution, a very wide angle offield, and a compact size are realized at the same time.

Table 48 shows values of Expressions (1), (2), and (4) of the imagingapparatus of this example.

TABLE 48 Conditional expression (1) f_sys/d_pup 1.03 Conditionalexpression (2) |R_img|/f_sys 1.02 Conditional expression (4)|R_img|/d_pup 1.05

The value of Expression (1) is 1.03 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemin the image side of the aperture stop can be close to a point symmetrystructure, and hence coma, astigmatism, and lateral chromatic aberrationcan be appropriately corrected.

The value of Expression (2) is 1.02 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a wide angle of field of 120.0 (degrees).

When Expressions (1) and (2) are satisfied, focus adjustment can beperformed from infinity to a close distance only by changing thedistance between the imaging optical system and the image plane withoutchanging the image plane shape.

In addition, in the imaging apparatus of this embodiment, a radius ofcurvature of the image plane is set substantially equal to the distancefrom the exit pupil to the image plane of the imaging optical system.

The value of Expression (4) is 1.05 and satisfies the range ofExpression (4).

Thus, the imaging optical system is close to a point symmetry structure,and hence coma, astigmatism, distortion, and lateral chromaticaberration are appropriately corrected. Further, focus adjustment can beperformed while maintaining high resolution in a wide focus adjustmentrange from infinity to a close distance.

Next, an action of improving the peripheral darkening is described.

In the imaging optical system of the imaging apparatus of this example,the radius of curvature of the image plane is set substantially equal tothe focal length of the imaging optical system so that the focal lengthcan be substantially uniform over the full angle of field.

Thus, the peripheral light intensity ratio can be improved by the squareof cos ω.

The largest half angle of field in this example is ω=60.0 (degrees) sothat cos² ω is 0.25 in contrast to cos⁴ ω=0.0625. Thus, peripheral lightintensity can be improved by 4 times.

When Expression (2) is satisfied, it is possible to obtain a reasonableeffect.

Further, in the imaging optical system of the imaging apparatus of thisexample, the radius of curvature of the image plane is set substantiallyequal to the distance from the exit pupil to the image plane of theimaging optical system, and hence the incident angle to the image planecan be set substantially orthogonal.

Thus, the peripheral light intensity ratio can be improved by the firstpower of cos ω.

The largest half angle of field in this example is ω=60.0 (degrees) sothat cos³ ω is 0.125 in contrast to cos⁴ ω=0.0625. Thus, peripherallight intensity can be improved by 2 times.

When Expression (4) is satisfied, it is possible to obtain a reasonableeffect.

When Expressions (2) and (4) are satisfied at the same time, theperipheral light intensity ratio can be improved by the third power ofcos ω, and the peripheral light intensity can be increased to be 8 timesthe conventional value.

Thus, because the peripheral light intensity ratio of the imagingoptical system having a wide angle of field can be significantlyimproved, it is possible to provide the imaging apparatus that can takea high quality image with high contrast and little noise over a wideangle of field.

As described above, using the effect of this embodiment, it is possibleto realize the imaging apparatus having good imaging performance over awide angle of field even at an F value smaller than F/2.0 with a compactstructure.

In addition, the peripheral darkening can be significantly improved, andhence it is possible to realize the imaging optical system that is verybright over a wide angle of field.

Thus, because the exposure time can be significantly shortened, it ispossible to provide the imaging apparatus that can take a high qualityimage in which blur due to shaking, image blur due to movement ofobject, and noise are appropriately reduced.

In addition, it is possible to provide an imaging optical system inwhich a defocused subject can be significantly blurred even with acompact structure.

Further, using the above-mentioned high performance imaging opticalsystem with the simple structure, focus adjustment can be performed withlittle deterioration of imaging performance in a wide range frominfinity to a close distance.

Example 13

In Example 13, a structural example of an imaging apparatus having aform different from that of Example 12 is described.

An imaging optical system used in an imaging apparatus of this exampleincludes three lenses G1, G2, and G3 and the aperture stop STO asillustrated in FIG. 55.

The imaging optical system includes, in order from the object side: afirst lens G1 as a plano-convex lens having a concave surface facing theobject side; a second lens G2 as a plano-convex lens having a convexsurface facing the image side; and a third lens G3 as a meniscus lenshaving a convex surface facing the image side.

In FIG. 55, IMG represents the image plane.

As illustrated in FIG. 55, the image plane IMG of the imaging apparatusaccording to this example is the incident surface of the opticaltransmission unit OTM formed into a sphere shape, which is formed alongthe field curvature of the imaging optical system. Therefore, good imageformation is realized over the entire region of the image plane IMG.

The optical transmission unit OTM of the imaging apparatus according tothis example is an image fiber formed of bound optical fibers of a fewmicron pitch and has a role of transmitting an image formed on the imageplane of the imaging optical system to the image sensor ICD.

The exit surface of the optical transmission unit OTM is formed to be aflat surface so as to be in intimate contact with the image sensor ICDfor connection. Thus, an image sensor unit ICU is formed.

Table 49 shows a structure of the imaging apparatus of this example.

Surface number 1 is the incident surface of the first lens G1. Surfacenumber 2 is the cemented surface between the exit surface of the firstlens G1 and the incident surface of the second lens G2. The lightblocking member is disposed in the non-effective part in the plane ofthe surface number 2 so as to constitute the aperture stop STO.

Surface number 3 is the cemented surface between the exit surface of thesecond lens G2 and the incident surface of the third lens G3. Surfacenumber 4 is the exit surface of the third lens G3 having a rotationsymmetry aspherical shape expressed by the polynomial of Expression(11).

Surface number 5 is the image plane IMG, which is the incident surfaceof the optical transmission unit OTM. Further, the exit surface of theoptical transmission unit OTM (not shown) is connected to the imagingelement ICD.

In Table 49, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number. Note that, the surface with a mark “(a)” isan aspherical surface.

TABLE 49 Configuration table Surface number R d Nd νd 1 3.1614 3.15531.89070 39.0 2 (STO) Flat 1.0594 1.89070 39.0 surface 3 −1.0655 2.22192.00170 21.8 4 −2.9424(a) 0.3520 5 (IMG) −3.6656

The aspherical surface coefficients of surface number 4 of the imagingapparatus of this example are shown in Table 50.

TABLE 50 Aspherical surface coefficients (Surface number 4) ParameterSymbol Value Conic constant K −1.66411E+00 Fourth order coefficient A5.83546E−03 Sixth order coefficient B −3.55248E−03 Eighth ordercoefficient C 4.46561E−04 Tenth order coefficient D −2.33467E−05

In the imaging apparatus of this example, the lens surface closest tothe image side is formed to be an aspherical surface.

FIG. 56A illustrates an aspherical shape of the lens surface closest tothe image side, and FIG. 56B illustrates an aspherical amount of thelens surface closest to the image side. In addition, FIG. 57Aillustrates second order differential values of the aspherical surfaceand the reference spherical surface, and FIG. 57B illustrates the secondorder differential value of the aspherical component.

As illustrated in FIG. 56A, the lens surface closest to the image sidein this example is a lens surface having a sag amount increasing in thenegative direction from the optical axis toward the periphery, and is aconvex surface facing the image side.

The reference spherical surface of this lens surface is a sphericalsurface having a convex surface facing the image side and a radius ofcurvature R=−2.9424 (mm).

FIG. 56B illustrates the aspherical amount.

As illustrated in FIG. 56B, in this example, the aspherical amount isdisplaced in the positive direction, and the aspherical surface isdisplaced from the reference spherical surface to the image side, namelyto the outside of the imaging optical system.

Further, the aspherical amount of the imaging optical system displacedto the outside is gradually increased as being away from the opticalaxis so as to give the largest aspherical amount in the periphery of thelens surface.

FIG. 57A illustrates the second order differential value of theaspherical surface by a solid line and the second order differentialvalue of the reference spherical surface by a broken line.

Both the second order differential value of the aspherical surface andthe second order differential value of the reference spherical surfacehave negative values.

FIG. 57B illustrates the second order differential value of theaspherical component.

The second order differential value of the aspherical component isincreased gradually in the positive direction as being away from theoptical axis.

In this way, the aspherical component having a positive second orderdifferential value is given to the reference spherical surface having anegative second order differential value. Thus, the second orderdifferential value in the periphery of the lens surface is reduced to besmaller than that of the reference spherical surface.

Expression (24) indicates a relationship between the second orderdifferential value and the power.

On the lens surface closest to the image side in the imaging opticalsystem, the medium on the object side of the lens surface is opticalglass having N=2.00170, and the medium on the image side of the lenssurface is air having N′=1.0000. Therefore, (N′−N) has a negative value.

Therefore, the lens surface closest to the image side has the lenssurface shape having positive power on the optical axis which isgradually decreased as being away from the optical axis.

Thus, spherical aberration can be appropriately corrected.

In particular, when the lens surface closest to the image side has theaspherical surface having the aspherical amount displaced from thereference spherical surface to the outside of the imaging optical systemin the periphery of the lens surface, spherical aberration of the fieldangle light beam in a wide field angle region can be appropriatelycorrected.

FIG. 58 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 59 illustrates a lateral aberrationdiagram thereof. As illustrated in FIG. 58, spherical aberration, axialchromatic aberration, astigmatism, field curvature, and chromaticspherical aberration are appropriately corrected. In particular, thelight beam in the entire region from a low incident light beam height toa high incident light beam height can be condensed on the image plane,and hence spherical aberration can be very appropriately corrected.

In addition, axial chromatic aberration and chromatic sphericalaberration are also very appropriately corrected so that high imagingperformance is obtained.

As illustrated in FIG. 59, good performance is obtained in each fieldangle light beam, and coma, field curvature, and lateral chromaticaberration are appropriately corrected.

Table 51 shows the specifications of the imaging apparatus of thisexample.

TABLE 51 Focal length of f_sys 3.600 (mm) imaging optical system F valueF/# 1.20 Angle of field 2ω 120.0 (deg) Entire length L_sys 6.437 (mm)Distance from exit d_pup 4.062 (mm) pupil to image plane

The imaging apparatus of this example has a small F value of F/1.2, avery wide angle of field of 120.0 (degrees), and a compact size with theentire length of 6.437 (mm), which is an example of the imagingapparatus in which brightness, high resolution, a very wide angle offield, and a compact size are realized at the same time.

TABLE 52 Conditional expression (1) f_sys/d_pup 0.89 Conditionalexpression (2) |R_img|/f_sys 1.02 Conditional expression (4)|R_img|/d_pup 0.90

Table 52 shows values of Expressions (1), (2), and (4) of the imagingapparatus of this example.

The value of Expression (1) is 0.89 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemfrom the aperture stop to the image side can be close to a pointsymmetry structure, and hence coma, astigmatism, distortion, and lateralchromatic aberration can be appropriately corrected.

The value of Expression (2) is 1.02 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a wide angle of field of 120.0 (degrees).

When Expressions (1) and (2) are satisfied, focus adjustment can beperformed from infinity to a close distance only by changing thedistance between the imaging optical system and the image plane whilenot changing the shape of the image plane.

The value of Expression (4) is 0.90 and satisfies the range ofExpression (4).

Thus, the imaging optical system is close to a point symmetry structure,and hence coma, astigmatism, distortion, and lateral chromaticaberration are appropriately corrected.

Further, focus adjustment can be performed while maintaining highresolution in a wide focus adjustment range from infinity to a closedistance.

Example 14

In Example 14, a structural example of an imaging apparatus having aform different from those of the above-mentioned examples is described.

An imaging optical system used in an imaging apparatus of this exampleincludes three lenses G1, G2, and G3 and the aperture stop STO asillustrated in FIG. 60.

The imaging optical system includes, in order from the object side: afirst lens G1 as a meniscus lens having a convex surface facing theobject side; a second lens G2 as a plano-convex lens having a convexsurface facing the image side; and a third lens G3 as a meniscus lenshaving a convex surface facing the image side.

In FIG. 60, IMG represents the image plane.

As illustrated in FIG. 60, the image plane IMG of the imaging apparatusaccording to this example is the incident surface of the opticaltransmission unit OTM formed into a sphere shape, which is formed alongthe field curvature of the imaging optical system. Therefore, good imageformation is realized over the entire region of the image plane IMG.

The optical transmission unit OTM of the imaging apparatus according tothis example is an image fiber formed of bound optical fibers of a fewmicron pitch and has a role of transmitting an image formed on the imageplane of the imaging optical system to the image sensor ICD.

The exit surface of the optical transmission unit OTM is formed to be aflat surface so as to be in intimate contact with the image sensor ICDfor connection. Thus, an image sensor ICD is constituted.

Table 53 shows a structure of the imaging apparatus of this example.

Surface number 1 is the incident surface of the first lens G1 having arotation symmetry aspherical shape expressed by the polynomial ofExpression (11).

Surface number 2 is the cemented surface between the exit surface of thefirst lens G1 and the incident surface of the second lens G2. The lightblocking member is disposed in the non-effective part in the plane ofthe surface number 2 so as to constitute the aperture stop STO. Surfacenumber 3 is the cemented surface between the exit surface of the secondlens G2 and the incident surface of the third lens G3. Surface number 4is the exit surface of the third lens G3 having a rotation symmetryaspherical shape expressed by the polynomial of Expression (11).

Surface number 5 is the image plane IMG, which is the incident surfaceof the optical transmission unit OTM. Further, the exit surface of theoptical transmission unit OTM (not shown) is connected to the imagesensor ICD.

In Table 53, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number. Note that, the surface with a mark “(a)” isan aspherical surface.

TABLE 53 Configuration table Surface number R d Nd νd 1 3.2643(a) 3.29741.88202 37.2 2 (STO) Flat 1.0627 1.88202 37.2 surface 3 −1.0664 2.01092.00270 19.3 4 −2.9174(a) 0.5118 5 (IMG) −3.5746

Table 54A shows aspherical surface coefficients of surface number 1 inthe imaging apparatus of this example, and Table 54B shows asphericalsurface coefficients of surface number 4.

TABLE 54A Aspherical surface coefficients (Surface number 1) ParameterSymbol Value Conic constant K −2.67630E−03 Fourth order coefficient A−1.66783E−04 Sixth order coefficient B 5.41266E−05 Eighth ordercoefficient C −7.27371E−06 Tenth order coefficient D 3.44022E−07

TABLE 54B Aspherical surface coefficient (Surface number 4) ParameterSymbol Value Conic constant K −9.09146E−01 Fourth order coefficient A−1.21019E−04 Sixth order coefficient B −1.78470E−03 Eighth ordercoefficient C 2.94879E−04 Tenth order coefficient D −2.53496E−05

In the imaging apparatus of this example, the lens surface closest tothe object side and the lens surface closest to the image side areformed as aspherical surfaces.

FIG. 61A shows an aspherical shape of the lens surface closest to theobject side, and FIG. 61B shows an aspherical amount of the lens surfaceclosest to the object side. In addition, FIG. 62A shows second orderdifferential values of the aspherical surface and the referencespherical surface, and FIG. 62B shows the second order differentialvalue of the aspherical component.

As shown in FIG. 61A, the lens surface closest to the object side inthis example is a lens surface having a sag amount increasing in thepositive direction from the optical axis toward the periphery, and aconvex surface facing the object side.

The reference spherical surface of this lens surface is a sphericalsurface having a convex surface facing the object side and a radius ofcurvature R=3.2643 (mm).

FIG. 61B shows the aspherical amount.

As shown in FIG. 61B, in this example, the aspherical amount isdisplaced in the negative direction, and the aspherical surface isdisplaced from the reference spherical surface to the object side,namely to the outside of the imaging optical system.

Further, the aspherical amount of the imaging optical system displacedto the outside is gradually increased as being away from the opticalaxis so as to give the largest aspherical amount in the periphery of thelens surface.

FIG. 62A shows the second order differential value of the asphericalsurface by a solid line and the second order differential value of thereference spherical surface by a broken line. Both the second orderdifferential value of the aspherical surface and the second orderdifferential value of the reference spherical surface have a positivevalue.

FIG. 62B shows the second order differential value of the asphericalcomponent.

The second order differential value of the aspherical component isincreased gradually in the negative direction as being away from theoptical axis.

In this way, the aspherical component having a negative second orderdifferential value is given to the reference spherical surface having apositive second order differential value. Thus, the second orderdifferential value in the periphery of the lens surface is reduced to besmaller than that of the reference spherical surface.

Expression (24) indicates a relationship between the second orderdifferential value and the power.

On the lens surface closest to the object side in the imaging opticalsystem, the medium on the object side of the lens surface is air havingN=1.0000, and the medium on the image side of the lens surface isoptical glass having N′=1.88202. Therefore, (N′−N) has a positive value.

Therefore, the lens surface closest to the object side is formed as thelens surface shape having positive power on the optical axis which isgradually decreased as being away from the optical axis.

Thus, spherical aberration can be appropriately corrected.

In particular, when the lens surface closest to the object side isformed as the aspherical surface having the aspherical amount displacedfrom the reference spherical surface to the outside of the imagingoptical system in the periphery of the lens surface, sphericalaberration of the field angle light beam in axial light and the vicinityof the axis can be appropriately corrected.

FIG. 63A shows an aspherical shape of the lens surface closest to theimage side, and FIG. 63B shows an aspherical amount of the lens surfaceclosest to the image side. In addition, FIG. 64A shows second orderdifferential values of the aspherical surface and the referencespherical surface, and FIG. 64B shows the second order differentialvalue of the aspherical component.

As shown in FIG. 63A, the lens surface closest to the image side in thisexample is a lens surface having a sag amount increasing in the negativedirection as being away from the optical axis toward the periphery, andis a convex surface facing the image side.

The reference spherical surface of this lens surface is a sphericalsurface having a convex surface facing the image side and a radius ofcurvature R=−2.9174 (mm).

FIG. 63B shows the aspherical amount.

As shown in FIG. 63B, in this example, the aspherical amount isdisplaced in the positive direction, and the aspherical surface isdisplaced from the reference spherical surface to the image side, namelyto the outside of the imaging optical system.

Further, the aspherical amount of the imaging optical system displacedto the outside is gradually increased as being away from the opticalaxis so as to give the largest aspherical amount in the periphery of thelens surface.

FIG. 64A shows the second order differential value of the asphericalsurface by a solid line and the second order differential value of thereference spherical surface by a broken line. Both the second orderdifferential value of the aspherical surface and the second orderdifferential value of the reference spherical surface have a negativevalue.

FIG. 64B shows the second order differential value of the asphericalcomponent.

The second order differential value of the aspherical component isincreased gradually in the positive direction as being away from theoptical axis.

In this way, the aspherical component having a positive second orderdifferential value is given to the reference spherical surface having anegative second order differential value. Thus, the second orderdifferential value in the periphery of the lens surface is reduced to besmaller than that of the reference spherical surface.

On the lens surface closest to the image side in the imaging opticalsystem, the medium on the object side of the lens surface is opticalglass having N=2.00270, and the medium on the image side of the lenssurface is air having N′=1.0000. Therefore, (N′−N) has a negative value.

Therefore, the lens surface closest to the image side is formed as thelens surface shape having positive power on the optical axis which isgradually decreased as being away from the optical axis.

Thus, spherical aberration can be appropriately corrected.

In particular, when the lens surface closest to the image side is formedas the aspherical surface having the aspherical amount displaced fromthe reference spherical surface to the outside of the imaging opticalsystem in the periphery of the lens surface, spherical aberration of thefield angle light beam in a wide field angle region can be appropriatelycorrected.

FIG. 65 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 66 illustrates a lateral aberrationdiagram thereof.

As illustrated in FIG. 65, spherical aberration, axial chromaticaberration, astigmatism, field curvature, and chromatic sphericalaberration are appropriately corrected. In particular, the light beam inthe entire region from a low incident light beam height to a highincident light beam height can be condensed on the image plane, andhence spherical aberration can be very appropriately corrected.

In addition, axial chromatic aberration and chromatic sphericalaberration are also very appropriately corrected so that high imagingperformance is obtained.

As illustrated in FIG. 66, good performance is obtained in each fieldangle light beam, and coma, field curvature, and lateral chromaticaberration are appropriately corrected.

As in this example, both the lens surface closest to the object side andthe lens surface closest to the image side are formed as the asphericalsurface having the aspherical amount displaced from the referencespherical surface to the outside of the imaging optical system in theperiphery of the lens surface. Thus, the spherical aberration can becorrected with high accuracy over a wide angle of field.

Table 55 shows the specifications of the imaging apparatus of thisexample.

TABLE 55 Focal length of f_sys 3.600 (mm) imaging optical system F valueF/# 1.20 Angle of field 2ω 120.0 (deg) Entire length L_sys 6.371 (mm)Distance from exit d_pup 3.760 (mm) pupil to image plane

The imaging apparatus of this example has a small F value of F/1.2, avery wide angle of field of 120.0 (degrees), and a compact size with theentire length of 6.371 (mm), which is an example of the imagingapparatus in which brightness, high resolution, a very wide angle offield, and a compact size are realized at the same time. Table 56 showsvalues of Expressions (1), (2), and (4) of the imaging apparatus of thisexample.

TABLE 56 Conditional expression (1) f_sys/d_pup 0.96 Conditionalexpression (2) |R_img|/f_sys 0.99 Conditional expression (4)|R_img|/d_pup 0.95

The value of Expression (1) is 0.96 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemin the image side of the aperture stop can be close to a point symmetrystructure, and hence coma, astigmatism, distortion, and lateralchromatic aberration can be appropriately corrected.

The value of Expression (2) is 0.99 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a wide angle of field of 120.0 (degrees).

The value of Expression (4) is 0.95 and satisfies the range ofExpression (4).

Thus, the imaging optical system is close to a point symmetry structure,and hence coma, astigmatism, distortion, and lateral chromaticaberration are appropriately corrected.

Further, in the imaging apparatus of this example, the distance betweenthe imaging optical system and the image plane is changed so as toperform focus adjustment.

Because Expression (4) is satisfied, focus adjustment can be performedwhile maintaining high resolution in a wide focus adjustment range frominfinity to a close distance.

Example 15

In Example 15, a structural example of an imaging apparatus having aform different from those of the above-mentioned examples is described.

The imaging optical system used in the imaging apparatus of this exampleincludes four lenses G1, G2, G3, and G4 and the aperture stop STO asillustrated in FIG. 67.

The imaging optical system includes, in order from the object side: thefirst lens G1 as the meniscus lens having a convex surface facing theobject side; the second lens G2 as the plano-convex lens having a convexsurface facing the object side; the third lens G3 as the plano-convexlens having a convex surface facing the image side; and the fourth lensG4 as the meniscus lens having a convex surface facing the image side.

In FIG. 67, IMG represents the image plane.

As illustrated in FIG. 67, the image plane IMG of the imaging apparatusaccording to this example is the image sensor ICD formed into a sphereshape on a deformable substrate.

Table 57 shows a structure of the imaging apparatus of this example.

Surface number 1 is the incident surface of the first lens G1 having therotation symmetry aspherical shape expressed by the polynomial ofExpression (11).

Surface number 2 is the cemented surface between the exit surface of thefirst lens G1 and the incident surface of the second lens G2. Surfacenumber 3 is the cemented surface between the exit surface of the secondlens G2 and the incident surface of the third lens G3, and the lightblocking member is disposed in the non-effective part in the plane ofthe surface number 3 so as to form the aperture stop STO.

Surface number 4 is the cemented surface between the exit surface of thethird lens G3 and the incident surface of the fourth lens G4. Surfacenumber 5 is the exit surface of the fourth lens G4 having a rotationsymmetry aspherical shape expressed by the polynomial of Expression(11).

Surface number 6 is the image plane IMG, which is the incident surfaceof the curved image sensor.

In Table 57, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number. Note that, the surface with a mark “(a)” isan aspherical surface.

TABLE 57 Surface number R d Nd νd 1 3.0198(a) 1.8417 2.00060 25.5 21.1768 1.1768 1.87801 38.5 3 (STO) Flat 1.1759 1.87801 38.5 surface 4−1.1759 1.8491 2.00060 25.5 5 −2.9057(a) 0.5912 6 (IMG) −3.6217

Table 58A shows aspherical surface coefficients of surface number 1 andTable 58B shows aspherical surface coefficients of surface number 5 inthe imaging apparatus of this example.

TABLE 58A Aspherical surface coefficient (Surface number 1) ParameterSymbol Value Conic constant K −1.53715E−03 Fourth order coefficient A−1.50377E−04 Sixth order coefficient B 6.34809E−05 Eighth ordercoefficient C −1.00126E−05 Tenth order coefficient D 5.64238E−07

TABLE 58B Aspherical surface coefficient (Surface number 5) ParameterSymbol Value Conic constant K −1.07977E−01 Fourth order coefficient A2.66867E−03 Sixth order coefficient B −6.82422E−04 Eighth ordercoefficient C 1.11698E−04 Tenth order coefficient D −7.68079E−06

In the imaging apparatus of this example, the lens surface closest tothe object side and the lens surface closest to the image side areformed as aspherical surfaces.

FIG. 68A shows an aspherical shape of the lens surface closest to theobject side, and FIG. 68B shows an aspherical amount of the lens surfaceclosest to the object side. In addition, FIG. 69A shows second orderdifferential values of the aspherical surface and the referencespherical surface, and FIG. 69B shows the second order differentialvalue of the aspherical component.

As shown in FIG. 68A, the lens surface closest to the object side inthis example is a lens surface having a sag amount increasing in thepositive direction from the optical axis toward the periphery, and is aconvex surface facing the object side.

The reference spherical surface of this lens surface is a sphericalsurface having a convex surface facing the object side and a radius ofcurvature R=3.0198 (mm).

FIG. 68B shows the aspherical amount.

As shown in FIG. 68B, in this example, the aspherical amount isdisplaced in the negative direction, and the aspherical surface isdisplaced from the reference spherical surface to the object side,namely to the outside of the object pickup optical system.

Further, the aspherical amount displaced to the outside of the imagingoptical system is gradually increased as being away from the opticalaxis so as to give the largest aspherical amount in the periphery of thelens surface.

FIG. 69A shows the second order differential value of the asphericalsurface by a solid line and the second order differential value of thereference spherical surface by a broken line. Both the second orderdifferential value of the aspherical surface and the second orderdifferential value of the reference spherical surface have a positivevalue.

FIG. 69B shows the second order differential value of the asphericalcomponent.

The second order differential value of the aspherical component isincreased gradually in the negative direction as being away from theoptical axis.

In this way, the aspherical component having a negative second orderdifferential value is given to the reference spherical surface having apositive second order differential value. Thus, the second orderdifferential value in the periphery of the lens surface is reduced to besmaller than that of the reference spherical surface.

Expression (24) indicates a relationship between the second orderdifferential value and the power.

On the lens surface closest to the object side in the imaging opticalsystem, the medium on the object side of the lens surface is air havingN=1.0000, and the medium on the image side of the lens surface isoptical glass having N′=2.00060. Therefore, (N′−N) has a positive value.

Therefore, the lens surface closest to the object side is formed as thelens surface shape having positive power on the optical axis which isgradually decreased as being away from the optical axis.

Thus, spherical aberration can be appropriately corrected.

In particular, when the lens surface closest to the object side isformed as the aspherical surface having the aspherical amount displacedfrom the reference spherical surface to the outside of the imagingoptical system in the periphery of the lens surface, sphericalaberration of the field angle light beam in axial light and a vicinityof the axis can be appropriately corrected.

FIG. 70A shows an aspherical shape of the lens surface closest to theimage side, and FIG. 70B shows an aspherical amount of the lens surfaceclosest to the image side.

In addition, FIG. 71A shows second order differential values of theaspherical surface and the reference spherical surface, and FIG. 71Bshows the second order differential value of the aspherical component.

As shown in FIG. 70A, the lens surface closest to the image side in thisexample is a lens surface having a sag amount increasing in the negativedirection from the optical axis toward the periphery, and is a convexsurface facing the image side.

The reference spherical surface of this lens surface is a sphericalsurface having a convex surface facing the image side and a radius ofcurvature R=−2.9057 (mm).

FIG. 70B shows the aspherical amount.

As shown in FIG. 70B, in this example, the aspherical amount isdisplaced in the positive direction, and the aspherical surface isdisplaced from the reference spherical surface to the image side, namelyto the outside of the imaging optical system.

Further, the aspherical amount displaced to the outside of the imagingoptical system is gradually increased as being away from the opticalaxis so as to give the largest aspherical amount in the periphery of thelens surface.

FIG. 71A shows the second order differential value of the asphericalsurface by a solid line and the second order differential value of thereference spherical surface by a broken line. Both the second orderdifferential value of the aspherical surface and the second orderdifferential value of the reference spherical surface have a negativevalue.

FIG. 71B shows the second order differential value of the asphericalcomponent.

The second order differential value of the aspherical component isincreased gradually in the positive direction as being away from theoptical axis.

In this way, the aspherical component having a positive second orderdifferential value is given to the reference spherical surface having anegative second order differential value. Thus, the second orderdifferential value in the periphery of the lens surface is reduced to besmaller than that of the reference spherical surface.

On the lens surface closest to the image side in the imaging opticalsystem, the medium on the object side of the lens surface is opticalglass having N=2.00060, and the medium on the image side of the lenssurface is air having N′=1.0000. Therefore, (N′−N) has a negative value.

Therefore, the lens surface closest to the image side is formed as thelens surface shape having positive power on the optical axis which isgradually decreased as being away from the optical axis.

Thus, spherical aberration can be appropriately corrected.

In particular, when the lens surface closest to the image side is formedas the aspherical surface having the aspherical amount displaced fromthe reference spherical surface to the outside of the imaging opticalsystem in the periphery of the lens surface, spherical aberration of thefield angle light beam in a wide field angle region can be appropriatelycorrected.

FIG. 72 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 73 illustrates a lateral aberrationdiagram thereof.

As illustrated in FIG. 72, spherical aberration, axial chromaticaberration, astigmatism, field curvature, and chromatic sphericalaberration are very appropriately corrected. In particular, the lightbeam in the entire region from a low incident light beam height to ahigh incident light beam height can be condensed on the image plane, andhence spherical aberration can be very appropriately corrected.

In addition, axial chromatic aberration and chromatic sphericalaberration are also very appropriately corrected so that high imagingperformance is obtained.

As illustrated in FIG. 73, good performance is obtained in each fieldangle light beam, and coma, field curvature, and lateral chromaticaberration are very appropriately corrected.

As in this example, both the lens surface closest to the object side andthe lens surface closest to the image side are formed as the asphericalsurfaces to which the aspherical amount displaced from the referencespherical surface to the outside of the imaging optical system in theperiphery of the lens surface is given. Thus, the spherical aberrationcan be corrected with high accuracy over a wide angle of field.

Table 59 shows the specifications of the imaging apparatus of thisexample.

TABLE 59 Focal length of f_sys 3.600 (mm) imaging optical system F valueF/# 1.20 Angle of field 2ω 120.0 (deg) Entire length L_sys 6.044 (mm)Distance from exit d_pup 3.616 (mm) pupil to image plane

The imaging apparatus of this example has a small F value of F/1.2, avery wide angle of field of 120.0 (degrees), and a compact size with theentire length of 6.044 (mm), which is an example of the imagingapparatus in which brightness, high resolution, a very wide angle offield, and a compact size are realized at the same time. Table 60 showsvalues of Expressions (1), (2), and (4) of the imaging apparatus of thisexample.

TABLE 60 Conditional expression (1) f_sys/d_pup 0.96 Conditionalexpression (2) |R_img|/f_sys 1.01 Conditional expression (4)|R_img|/d_pup 0.97

The value of Expression (1) is 0.96 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemin the image side of the aperture stop can be close to a point symmetrystructure, and hence coma, astigmatism, distortion, and lateralchromatic aberration can be appropriately corrected.

The value of Expression (2) is 1.01 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a wide angle of field of 120.0 (degrees).

The value of Expression (4) is 0.97 and satisfies the range ofExpression (4).

Thus, the imaging optical system is close to a point symmetry structure,and hence coma, astigmatism, and lateral chromatic aberration areappropriately corrected.

Further, in the imaging apparatus of this example, the distance betweenthe imaging optical system and the image plane is changed so as toperform focus adjustment. Because Expression (4) is satisfied, focusadjustment can be performed while maintaining high resolution in a widefocus adjustment range from infinity to a close distance.

Example 16

In Example 16, a structural example of an imaging apparatus having aform different from those of the above-mentioned examples is described.

An imaging optical system used in an imaging apparatus of this exampleincludes four lenses G1, G2, G3, and G4 and the aperture stop STO asillustrated in FIG. 74.

The imaging optical system includes, in order from the object side: thefirst lens G1 as the meniscus lens having a convex surface facing theobject side; the second lens G2 as the plano-convex lens having a convexsurface facing the object side; the third lens G3 as the plano-convexlens having a convex surface facing the image side; and the fourth lensG4 as the meniscus lens having a convex surface facing the image side.

In addition, similarly to Example 12, the imaging unit ICU including theoptical transmission unit OTM and the flat surface image sensor ICD isused.

In this example, only the lens surface closest to the image side in theimaging optical system is formed as the aspherical surface.

Table 61 shows a structure of the imaging apparatus of this example.

In Table 61, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number. Note that, the surface with a mark “(a)” isan aspherical surface.

TABLE 61 Configuration table Surface number R d Nd νd 1 3.1612 2.00281.92286 21.3 2 1.1490 1.1490 1.89800 34.0 3 (STO) Flat 1.0577 1.8980034.0 surface 4 −1.0843 2.1748 2.00060 25.5 5 −3.0745(a) 0.3873 6 (IMG)−3.6937

The aspherical surface coefficients of surface number 5 of the imagingapparatus of this example are shown in Table 62.

TABLE 62 Aspherical surface coefficients (Surface number 5) ParameterSymbol Value Conic constant K −2.76669E−01 Fourth order coefficient A7.28040E−03 Sixth order coefficient B −1.87130E−03 Eighth ordercoefficient C 2.18939E−04 Tenth order coefficient D −1.07514E−05

FIG. 75A shows an aspherical shape of the lens surface closest to theimage side, and FIG. 75B shows an aspherical amount. FIG. 76A showssecond order differential values of the aspherical surface and thereference spherical surface, and FIG. 76B shows the second orderdifferential value of the aspherical component.

As shown in FIG. 75A, the lens surface closest to the image side(surface number 5) of this example is a lens surface having a sag amountincreasing in the negative direction from the optical axis to theperiphery and is a lens surface having a convex surface facing the imageside. This lens surface has the reference spherical surface that is aspherical surface having a radius of curvature R=−3.0745 (mm).

In addition, as shown in FIG. 75B, the aspherical amount is displaced inthe positive direction, and the aspherical surface is displaced from thereference spherical surface to the image side, namely to the outside ofthe imaging optical system. Then, the aspherical amount displaced to theoutside of the imaging optical system is gradually increased as beingaway from the optical axis, and the largest aspherical amount is givenin the periphery of the lens surface.

FIG. 76A shows the second order differential value of the asphericalsurface by a solid line and the second order differential value of thereference spherical surface by a broken line. Both the second orderdifferential value of the aspherical surface and the second orderdifferential value of the reference spherical surface are negative. FIG.76B shows the second order differential value of the asphericalcomponent.

The second order differential value of the aspherical component isgradually increased in the positive direction as being away from theoptical axis.

In this way, by giving the aspherical surface having a negative secondorder differential value of the reference spherical surface and apositive second order differential value of the aspherical component,the second order differential value in the periphery of the lens surfaceis reduced to be smaller than that of the reference spherical surface.

In other words, the reference spherical surface has positive power whilethe aspherical component has negative power, and power of the lenssurface is gradually reduced from the optical axis toward the peripheryof the lens surface.

Thus, because spherical aberration in the field angle light beam can beappropriately corrected, it is possible to provide the imaging apparatushaving good imaging performance over a wide angle of field.

In particular, in a wide field angle imaging optical system in which aperipheral light ray (upper ray) of the field angle light beam of thelargest angle of field passes through the lens surface closest to theobject side below the optical axis in the imaging optical system, theeffect of this embodiment is sufficiently exerted.

Table 63 shows the specifications of the imaging apparatus of thisexample.

TABLE 63 Focal length of f_sys 3.600 (mm) imaging optical system F valueF/# 1.20 Angle of field 2ω 120.0 (deg) Entire length L_sys 6.384 (mm)Distance from exit d_pup 3.620 (mm) pupil to image plane

The imaging apparatus of this example has a small F value of F/1.2, avery wide angle of field of 120.0 (degrees), and a compact size with theentire length of 6.384 (mm), which is an example of the imagingapparatus in which brightness, high resolution, a very wide angle offield, and a compact size are realized at the same time.

Table 64 shows values of Expressions (1), (2), and (4) of the imagingapparatus of this example.

TABLE 64 Conditional expression (1) f_sys/d_pup 0.95 Conditionalexpression (2) |R_img|/f_sys 1.03 Conditional expression (4)|R_img|/d_pup 0.97

The value of Expression (1) is 0.95 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemin the image side of the aperture stop can be close to a point symmetrystructure, and hence coma, astigmatism, distortion, and lateralchromatic aberration can be appropriately corrected.

The value of Expression (2) is 1.03 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a wide angle of field of 120.0 (degrees).

The value of Expression (4) is 0.97 and satisfies the range ofExpression (4).

Thus, the imaging optical system is close to a point symmetry structure,and hence coma, astigmatism, distortion, and lateral chromaticaberration are appropriately corrected.

FIG. 77 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 78 illustrates a lateral aberrationdiagram thereof.

Further, in the imaging apparatus of this example, the distance betweenthe imaging optical system and the image plane is changed so as toperform focus adjustment.

Because Expression (4) is satisfied, focus adjustment can be performedwhile maintaining high resolution in a wide focus adjustment range frominfinity to a close distance.

Example 17

In Example 17, a structural example of an imaging apparatus having aform different from those of the above-mentioned examples is described.

The imaging optical system used in the imaging apparatus of this exampleincludes four lenses G1, G2, G3, and G4 and the aperture stop STO asillustrated in FIG. 79.

The imaging optical system includes, in order from the object side: thefirst lens G1 as the meniscus lens having a convex surface facing theobject side; the second lens G2 as the plano-convex lens having a convexsurface facing the object side; the third lens G3 as the plano-convexlens having a convex surface facing the image side; and the fourth lensG4 as the meniscus lens having a convex surface facing the image side.

In addition, similarly to Example 12, the imaging unit ICU including theoptical transmission unit OTM and the flat surface image sensor ICD isused.

In this example, only the lens surface closest to the object side in theimaging optical system is formed as the aspherical surface.

Table 65 shows a structure of the imaging apparatus of this example.

In Table 65, R represents a radius of curvature (mm), d represents asurface interval (mm), Nd represents a d-line refractive index, and νdrepresents an Abbe number. Note that, the surface with a mark “(a)” isan aspherical surface.

TABLE 65 Configuration table Surface number R d Nd νd 1 3.1360(a) 1.98411.92286 21.3 2 1.1395 1.1395 1.89800 34.0 3 (STO) Flat 1.0379 1.8980034.0 surface 4 −1.0959 2.1193 2.00060 25.5 5 −3.4770 0.4145 6 (IMG)−3.7474

The aspherical surface coefficients of surface number 1 of the imagingapparatus of this example are shown in Table 66.

TABLE 66 Aspherical surface coefficients (Surface number 1) ParameterSymbol Value Conic constant K −6.25796E−03 Fourth order coefficient A−1.74593E−04 Sixth order coefficient B 5.66974E−05 Eighth ordercoefficient C −8.24266E−06 Tenth order coefficient D 4.34369E−07

FIG. 80A shows an aspherical shape of the lens surface closest to theobject side, and FIG. 80B shows an aspherical amount. FIG. 81A showssecond order differential values of the aspherical surface and thereference spherical surface, and FIG. 81B shows the second orderdifferential value of the aspherical component.

As shown in FIG. 80A, the lens surface closest to the object side(surface number 1) of this example is a lens surface having a sag amountincreasing in the positive direction from the optical axis toward theperiphery and is a lens surface having a convex surface facing theobject side. This lens surface has the reference spherical surface thatis a spherical surface having a radius of curvature R=−3.1360 (mm).

As shown in FIG. 80B, the aspherical amount is displaced in the negativedirection, and the aspherical surface is displaced from the referencespherical surface to the object side, namely to the outside of theimaging optical system.

Then, the aspherical amount displaced to the outside of the imagingoptical system is gradually increased as being away from the opticalaxis, and the largest aspherical amount is given in the periphery of thelens surface.

FIG. 81A shows the second order differential value of the asphericalsurface by a solid line and the second order differential value of thereference spherical surface by a broken line. Both the second orderdifferential value of the aspherical surface and the second orderdifferential value of the reference spherical surface are positive.

FIG. 81B shows the second order differential value of the asphericalcomponent.

The second order differential value of the aspherical component isgradually increased in the negative direction as being away from theoptical axis.

In this way, by giving the aspherical surface having a positive secondorder differential value of the reference spherical surface and anegative second order differential value of the aspherical component,the second order differential value in the periphery of the lens surfaceis reduced to be smaller than that of the reference spherical surface.

In other words, the reference spherical surface has positive power whilethe aspherical component has negative power, and power of the lenssurface is gradually reduced from the optical axis toward the peripheryof the lens surface.

Thus, because spherical aberration in the axial light can beappropriately corrected, it is possible to provide the imaging apparatushaving good imaging performance.

Table 67 shows the specifications of the imaging apparatus of thisexample.

TABLE 67 Focal length of f_sys 3.600 (mm) imaging optical system F valueF/# 1.20 Angle of field 2ω 120.0 (deg) Entire length L_sys 6.281 (mm)Distance from exit d_pup 3.572 (mm) pupil to image plane

The imaging apparatus of this example has a small F value of F/1.2, avery wide angle of field of 120.0 (degrees), and a compact size with theentire length of 6.281 (mm), which is an example of the imagingapparatus in which brightness, high resolution, a very wide angle offield, and a compact size are realized at the same time.

Table 68 shows values of Expressions (1), (2), and (4) of the imagingapparatus of this example.

TABLE 68 Conditional expression (1) f_sys/d_pup 1.09 Conditionalexpression (2) |R_img|/f_sys 1.04 Conditional expression (4)|R_img|/d_pup 1.13

The value of Expression (1) is 1.09 and satisfies the range ofExpression (1). Thus, the optical system of the imaging optical systemin the image side of the aperture stop can be close to a point symmetrystructure, and hence coma, astigmatism, distortion, and lateralchromatic aberration can be appropriately corrected.

The value of Expression (2) is 1.04 and satisfies the range ofExpression (2). Thus, field curvature and astigmatism can beappropriately corrected over a wide angle of field of 120.0 (degrees).

The value of Expression (4) is 1.13 and satisfies the range ofExpression (4).

Thus, the imaging optical system is close to a point symmetry structure,and hence coma, astigmatism, distortion, and lateral chromaticaberration are appropriately corrected.

FIG. 82 illustrates an axial aberration diagram of the imaging opticalsystem of this example, and FIG. 83 illustrates a lateral aberrationdiagram thereof.

Further, in the imaging apparatus of this example, the distance betweenthe imaging optical system and the image plane is changed so as toperform focus adjustment. Because Expression (4) is satisfied, focusadjustment can be performed while maintaining high resolution in a widefocus adjustment range from infinity to a close distance.

The present invention including the examples described above can beapplied to a product using the imaging apparatus such as a digitalcamera, a digital video camera, a cell phone camera, and a monitoringcamera.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.Japanese Patent Applications No. 2012-081540, filed Mar. 30, 2012, No.2012-081495, filed Mar. 30, 2012, No. 2012-081584, filed Mar. 30, 2012,and No. 2012-081634, filed Mar. 30, 2012 which are hereby incorporatedby reference herein in their entirety.

What is claimed is:
 1. An imaging apparatus comprising: an imagingoptical system including (a) an aperture stop, (b) a first opticalsystem disposed on an object side of the aperture stop, and (c) a secondoptical system disposed on an image side of the aperture stop; and alight-receiving surface which is disposed on an image side of theimaging optical system and is a concave surface facing the imagingoptical system, wherein the first optical system and the second opticalsystem have different positive power, wherein the first optical systemincludes a first lens closest to the object side and a second lensadjacent to the first lens, wherein the second optical system includes athird lens closest to the image side and a fourth lens adjacent to thethird lens, wherein a difference between an Abbe number of the thirdlens and an Abbe number of the fourth lens is larger than a differencebetween an Abbe number of the first lens and an Abbe number of thesecond lens, and wherein the following conditional expressions aresatisfied:0.8≦|R _(img) |/f _(sys)≦1.5, and0.8≦|R _(img) |/d _(pup)≦1.5 where f_(sys) represents a focal length ofthe imaging optical system, d_(pup) represents a distance from an exitpupil of the imaging optical system to the light-receiving surface, andR_(img) represents a radius of curvature of the light-receiving surface.2. The image pickup apparatus according to claim 1, further comprisingan image sensor including the light-receiving surface.
 3. The imagepickup apparatus according to claim 1, further comprising an opticaltransmission unit including the light-receiving surface.
 4. The imagepickup apparatus according to claim 1, wherein the following expressionis satisfied:1.850000≦Nd≦2.300000, where Nd represents a refractive index of at leastone of the first lens and the third lens.